Showing papers on "Path graph published in 2020"

Efficient fault-tolerant routing in IoT wireless sensor networks based on path graph flow modeling with Marchenko–Pastur distribution (EFT-PMD)

Abstract: In the internet of things (IoT) based wireless sensor network (WSN), the nodes are scattered to segregate the rapt data in the relevant field of application. In general, sensor nodes of IoT possess heterogeneous property and display cluster-based routing to transmit the data as it is considered as an efficient routing method. When one or more cluster heads (CHs) fail, the sensed data of sensor nodes that are currently serving cannot be forwarded by the faulty CHs. Consequently, data of the IoT application will not be sufficiently sensed by the sink node (gateway). As a result, information processing of this field will be affected profusely. This paper focuses on the development of a paired cluster fault-tolerant disjoint path routing in a path graph and a novel approach to solve this dilemma in polynomial time of the degree of the graph. The objective of this proposed IoT–WSN architecture is to diminish the latency, end-to-end delay as well as energy consumption and thereby improving the performance in terms of throughput and packet delivery ratio. The performance of this proposed method in IoT–WSN network is measured and affirmed using benchmark network simulator.

Control Distance and Energy Scaling of Complex Networks

Abstract: It has recently been shown that the average energy required to control a subset of target nodes in a complex network scales exponentially with the cardinality of the subset. While the mean scales exponentially, the variance of the control energy over different subsets of target nodes can be large and has, as of yet, not been explained. Here, we provide an explanation of the large variance as a result of both the length of the path that connects control inputs to the target nodes and the redundancy of paths of shortest length. Our first result provides an upper bound of the control energy as a function of path length between driver node and target node along an infinite path graph for a single target node. We also show that the energy estimate is still very accurate even when finite size effects are taken into account. Our second result refines the upper bound, by an order of magnitude or more, taking into account not only the length of the path, but also the redundancy of paths. Finally, we lay out the foundations for a more accurate estimation of the control energy for the multi-target node and multi-driver node problem.

A network attack path prediction method using attack graph

Abstract: The prediction of intrusion intention of abnormal information in wireless network can effectively guarantee the security and stability of network. Traditional methods describe the relationship between different types of attacks. When building the model, only the path of the network nodes involved in the current attack behavior is considered, so the vulnerability of the network can not be analyzed in detail. Then, a network attack node path detection model based on attack graph is proposed. Firstly, according to the theory of attack graph, the network attack graph is defined, the right state of attacker is detected, the connection matrix of network is obtained, and the formal description of vulnerability, attack effect and attack premise is obtained. Then, the attack path graph is used to describe the transfer relationship between nodes, map the process of the attack from one host or vulnerability to the next host or vulnerability, and give the shortest path to achieve the attack intention. Further obtain the maximum possibility of intrusion under each attack path of the network, and build a network attack node path detection model based on the detection results. The experimental results show that the proposed model has high accuracy and effectively improves the efficiency of network security analysis.

An upper bound of radio k -coloring problem and its integer linear programming model

Abstract: For a positive integer k, a radio k-coloring of a simple connected graph G = (V(G), E(G)) is a mapping $$f:V(G) \to \{ 0,1,2, \ldots \}$$ such that $$|f(u) - \,f(v)| \ge k + 1 - d(u, \, v)$$ for each pair of distinct vertices u and v of G, where d(u, v) is the distance between u and v in G. The span of a radio k-coloring f, rck(f), is the maximum integer assigned by it to some vertex of G. The radio k-chromatic number, rck(G) of G is min{rck(f)}, where the minimum is taken over all radio k-colorings f of G. If k is the diameter of G, then rck(G) is known as the radio number of G. In this paper, we propose an improved upper bound of radio k-chromatic number for a given graph against the other which is due to Saha and Panigrahi (in: Arumugan, Smyth (eds) Combinatorial algorithms (IWOCA 2012). Lecure notes in computer science, vol 7643, Springer, Berlin, 2012). The computational study shows that the proposed algorithm overcomes the previous algorithm. We introduce a polynomial algorithm [differs from the other that is due to Liu and Zhu (SIAM J Discrete Math 19(3):610–621, 2005)] which determines the radio number of the path graph Pn. Finally, we propose a new integer linear programming model for the radio k-coloring problem. The computational study between the proposed algorithm and LINGO solver shows that the proposed algorithm overcomes LINGO solver.

On quadratic embedding constants of star product graphs

Abstract: A connected graph $G$ is of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently if the distance matrix is conditionally negative definite, or equivalently if the quadratic embedding constant $\mathrm{QEC}(G)$ is non-positive. For a finite star product of (finite or infinite) graphs $G=G_1\star\cdots \star G_r$ an estimate of $\mathrm{QEC}(G)$ is obtained after a detailed analysis of the minimal solution of a certain algebraic equation. For the path graph $P_n$ an implicit formula for $\mathrm{QEC}(P_n)$ is derived, and by limit argument $\mathrm{QEC}(\mathbb{Z})=\mathrm{QEC}(\mathbb{Z}_+)=-1/2$ is shown. During the discussion a new integer sequence is found.

A Linear-Time Algorithm for Discrete Radius Optimally Augmenting Paths in a Metric Space

Abstract: Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of $P$. Previously, the "continuous" version of the problem where a center may be a point in the interior of an edge of the graph was studied and a linear-time algorithm was known. Our "discrete" version of the problem has not been studied before. We present a linear-time algorithm for the problem.

The edit distance function of some graphs

Abstract: The edit distance function of a hereditary property $\mathscr{H}$ is the asymptotically largest edit distance between a graph of density $p\in[0,1]$ and $\mathscr{H}$. Denote by $P_n$ and $C_n$ the path graph of order $n$ and the cycle graph of order $n$, respectively. Let $C_{2n}^*$ be the cycle graph $C_{2n}$ with a diagonal, and $\widetilde{C_n}$ be the graph with vertex set $\{v_0, v_1, \ldots, v_{n-1}\}$ and $E(\widetilde{C_n})=E(C_n)\cup \{v_0v_2\}$. Marchant and Thomason determined the edit distance function of $C_6^{*}$. Peck studied the edit distance function of $C_n$, while Berikkyzy et al. studied the edit distance of powers of cycles. In this paper, by using the methods of Peck and Martin, we determine the edit distance function of $C_8^{*}$, $\widetilde{C_n}$ and $P_n$, respectively.

Study of some topological invariants of subdivided mk graphs

Abstract: An mk-graph of a graph G can be defined by taking m≥2 copies G1,..., Gm of a graph G in which every vertex ut of copy Gt is adjacent to a corresponding vertex vs of copy Gs. An mk-graph is represented by mk(G). In this research study, we discussed some degree based topological indices (connectivity indices) of subdivided mk-graph generated by path graph and comb graph. The closed formulas for computing various degree based topological indices of subdivided mk-graphs were presented.

Three-dimensional steerable discrete cosine transform with application to 3D image compression

Abstract: This work introduces the three-dimensional steerable discrete cosine transform (3D-SDCT), which is obtained from the relationship between the discrete cosine transform (DCT) and the graph Fourier transform of a signal on a path graph. One employs the fact that the basis vectors of the 3D-DCT constitute a possible eigenbasis for the Laplacian of the product of such graphs. The proposed transform employs a rotated version of the 3D-DCT basis. We then evaluate the applicability of the 3D-SDCT in the field of 3D medical image compression. We consider the case where we have only one pair of rotation angles per block, rotating all the 3D-DCT basis vectors by the same pair. The obtained results show that the 3D-SDCT can be efficiently used in the referred application scenario and it outperforms the classical 3D-DCT.

A Linear-Time Algorithm for Discrete Radius Optimally Augmenting Paths in a Metric Space

Abstract: Let P be a path graph of n vertices embedded in a metric space. We consider the problem of adding a new edge to P so that the radius of the resulting graph is minimized, where any center is constra...

Total rainbow connection number of n-Centipede graph and its line, square, and middle graph

Abstract: Let G = (V(G), E(G)) is a nontrivial and connected graph. A path P at G connecting two vertices u and v in a total-colored graph G is said to be a total-rainbow path between u and v if all elements in V(P) ∪ E(P), except for u and v, are assigned different colors. The total-colored graph G is said to be a rainbow connected if it has a total-rainbow total-path between every two vertices. The total-rainbow connected number of a graph G denoted by trc(G) is the smallest number of colors that needed to make the graph G be a total-rainbow connected. In this paper, we determine the exact value of trc(G) where G are Line, Square, and Middle of n-Centipede graph. n-Centipede graph is a graph of 2n vertices obtained by joining the bottoms of n-copies of the path graph P2 laid in a row with edge and it is denoted by Cn.

Power Domination Number On Shackle Operation with Points as Lingkage

Abstract: The Power dominating set is a minimum point of determination in a graph that can dominate the connected dots around it, with a minimum domination point. The smallest cardinality of a power dominating set is called a power domination number with the notation . The purpose of this study is to determine the Shackle operations graph value from several special graphs with a point as a link. The result operation graphs are: Shackle operation graph from Path graph , Shackle operation graph from Sikel graph , Shackle operation graph from Star graph . The method used in this paper is axiomatic deductive method in solving problems. Understanding the axiomatic method itself is a method of deductive proof principles that applies in mathematical logic by using theorems that already exist in solving a problem. In this paper begins by determining the paper object that is the Shackle point operations result graph. Next, determine the cardinality of these graphs. After that, determine the point that has the maximum degree on the graph as the dominator point of power domination. Then, check whether the nearest neighbor has two or more degrees and analyze its optimization by using a ceiling function comparison between zero forching with the greatest degree of graph. Thus it can be determined ϒp minimal and dominated. The results of the power domination number study on Shackle operation graph result with points as connectors are , for and ; , for and ; , for and .

On perfect colorings of infinite multipath graphs

Abstract: A coloring of vertices of a given graph is called perfect if the color structure of each ball of radius $1$ in the graph depends only on the color of the ball center. Let $n$ be a positive integer. We consider a lexicographic product of the infinite path graph and a graph $G$ that can be either the complete or empty graph on $n$ vertices. We give a complete description of perfect colorings with an arbitrary number of colors of such graph products.

Glue dispensing path control method and device, computer equipment and storage medium thereof

Abstract: The invention discloses a glue dispensing path control method and device, computer equipment and a storage medium thereof. The method comprises the steps of obtaining a path graph, recognizing the coordinates of all points on the path graph, generating a path table according to the coordinates of all points, reading the path table during glue dispensing, and controlling a glue dispensing needle tosequentially move according to the coordinates of all points in the path table so as to carry out glue dispensing. According to the glue dispensing path control method and device, the computer equipment and the storage medium thereof, for a user, only the path graph needs to be edited, the operation is simple, and the path graph is edited more intuitively, so that the glue dispensing path controlis accurate and reliable. In addition, the path graph can be modified and adjusted conveniently, and then the glue dispensing path control is adjusted.

A New Algorithm to Recognize Path Graphs.

Abstract: A Path Graph is the intersection graph of vertex paths in an undirected tree. We present a new algorithm to recognize Path Graphs. It has the same worst-case time complexity as the faster recognition algorithm known so far [A.A. Schaffer, A faster algorithm to recognize undirected path graphs, Discrete Applied Mathematics, 43 (1993), pp. 261-295.] but it has an easier and more intuitive implementation based on a new characterization of Path Graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, CoRR, abs/1911.09069, (2019).].

Solution of an Open Problem Concerning the Augmented Zagreb Index and Chromatic Number of Graphs

Abstract: Let $G$ be a graph containing no component isomorphic to the path graph of order $2$. Denote by $d_w$ the degree of a vertex $w$ in $G$. The augmented Zagreb index ($AZI$) of $G$ is the sum of the quantities $(d_ud_v/(d_u+d_v-2))^3$ over all edges $uv$ of $G$. Denote by $\mathcal{G}(n,\chi)$ the class of all connected graphs of a fixed order $n$ and with a fixed chromatic number $\chi$, where $n\ge5$ and $3\le \chi \le n-1$. The problem of finding graph(s) attaining the maximum $AZI$ in the class $\mathcal{G}(n,\chi)$ has been solved recently in [F. Li, Q. Ye, H. Broersma, R. Ye, MATCH Commun. Math. Comput. Chem. 85 (2021) 257--274] for the case when $n$ is a multiple of $\chi$. The present paper gives the solution of the aforementioned problem not only for the remaining case (that is, when $n$ is not a multiple of $\chi$) but also for the case considered in the aforesaid paper.

A New Algorithm to Recognize Path Graphs and Directed Path Graphs.

Abstract: A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. We present a new algorithm to recognize path graphs and directed path graphs. It has the same worst-case time complexity as the faster recognition algorithms known so far but it does not require complex data structures and it has an easy and intuitive implementation based on a new characterization of path graphs [N. Apollonio and L. Balzotti, A New Characterization of Path Graphs, arXiv:1911.09069, (2019).].

On star coloring of degree splitting of comb product graphs

Abstract: A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. Let G = (V,E) be a graph with V = S1 [ S2 [ S3 [ . . . [ St [ T where each Si is a set of all vertices of the same degree with at least two elements and T =V (G) − St i=1 Si. The degree splitting graph DS (G) is obtained by adding vertices w1,w2, . . .wt and joining wi to each vertex of Si for 1 i t. The comb product between two graphs G and H, denoted by G ⊲ H, is a graph obtained by taking one copy of G and |V (G)| copies of H and grafting the ith copy of H at the vertex o to the ith vertex of G. In this paper, we give the exact value of star chromatic number of degree splitting of comb product of complete graph with complete graph, complete graph with path, complete graph with cycle, complete graph with star graph, cycle with complete graph, path with complete graph and cycle with path graph.

Radio labeling on some corona graphs

Abstract: A Radio labeling c of G is an assignment of positive integers to the vertices of G satisfying |c(u) - c(v)| ≥ diam (G)+1 - d(u, v) for every two distinct vertices (u, v), where, diam G be the diameter of G and d(u, v) be the distance between two distinct vertices. If G has radio labeling with maximum {c(v): v ∈ V(G)} = k, then the smallest number k satisfying this condition is called the radio number of G and is denoted by rn(G). In this paper we investigate the Radio labeling for the graphs C3 ⊙ Pn, C4 ⊙ Pn and C5 ⊙ Pn when n ≥ 2, where ⊙, the corona product between the cycle graph and a path graph. Also we determine the radio number of these graphs.

Weighted abstract path graph database partitioning

Abstract: In partitioning a graph database, a plurality of vertices of the graph database is assigned to a plurality of nodes. The vertices of the graph database are connected by edges that indicate relationships between the vertices. One or more abstract paths between one or more vertices of the graph database are identified. Each abstract path is weighted based on a likelihood of a database query following the abstract path. The vertices of the graph database are assigned to the nodes according to the abstract paths between the vertices.

Ollivier Ricci-flow on weighted graphs

Abstract: We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by\cite{NLLG} in which the discrete time Ricci flow algorithm has been applied successfully as a discrete geometric approach in detecting complex networks. Our main result is the existence and uniqueness theorem for solutions to a continuous time normalized Ricci flow. We also display possible solutions to the Ricci flow on path graph and prove the Ricci flow on finite star graph with at least three leaves converges to constant-weighted star.

Application program quality identification method and device, computer equipment and storage medium

Abstract: The invention relates to an application program quality identification method and device, computer equipment and a storage medium. The method comprises the steps of obtaining a directed operation pathdiagram corresponding to an application set where a to-be-identified application is located, wherein the directed operation path diagram is obtained according to an operation sequence corresponding to the application program set in a preset time period; extracting features of neighbor nodes corresponding to target graph nodes from the directed operation path graph, and aggregating the extracted features to generate vector representation corresponding to the target graph nodes, wherein the target graph node is a graph node corresponding to the to-be-identified application program; and classifying the to-be-identified application programs according to the vector representation, and determining a quality identification result of the to-be-identified application programs according to an obtained classification result. By adopting the method, the accuracy of application program quality identification can be improved.

$P_{n}$-induced-saturated graphs exist for all $n \geq 6$

Abstract: Let $P_{n}$ be a path graph on $n$ vertices. We say that a graph $G$ is $P_{n}$-induced-saturated if $G$ contains no induced copy of $P_{n}$, but deleting any edge of $G$ as well as adding to $G$ any edge of $G^{c}$ creates such a copy. Martin and Smith (2012) showed that there is no $P_{4}$-induced-saturated graph. On the other hand, there trivially exist $P_{n}$-induced-saturated graphs for $n=2,3$. Axenovich and Csikos (2019) ask for which integers $n \geq 5$ do there exist $P_{n}$-induced-saturated graphs. Raty (2019) constructed such a graph for $n=6$, and Cho, Choi and Park (2019) later constructed such graphs for all $n=3k$ for $k \geq 2$. We show by a different construction that $P_{n}$-induced-saturated graphs exist for all $n \geq 6$, leaving only the case $n=5$ open.

Reengineering ILE: towards a model for adapting the learning path

Abstract: The main challenge faced by ILE is its ability to offer tools adapted to each learner allowing him to learn effectively by taking into account the different constraints. In this article, we describe an approach to adapting the learner's path adapted to his profile while respecting the time he has for learning and making sure to maximize his mark during the final exam. To achieve this objective, a double-layer adapted learning path graph is generated, the educational resources associated with the path identified, the selection of the most suitable resources for each step carried out and the overall time of the estimated path and the forecast score of the final test calculated. Thereafter, the graph of the generated path is re-evaluated at each learning step taken to best adapt it to the learner.