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Showing papers in "Discrete Mathematics, Algorithms and Applications in 2019"


Journal ArticleDOI
TL;DR: The third leap Zagreb index of a graph G is denoted as LM3(G) and is defined as∑b∈V (G) d(b/G)d2(b / G) d2( b/G), where d2 and d2 are the 2-distance degree and the degree of the vertex b in G.
Abstract: The third leap Zagreb index of a graph G is denoted as LM3(G) and is defined as LM3(G) =∑b∈V (G)d(b/G)d2(b/G), where d2(b/G) and d(b/G) are the 2-distance degree and the degree of the vertex b in G...

21 citations


Journal ArticleDOI
TL;DR: It is shown that the Gray image of skew constacyclic codes over finite non-chain ring ℛ = 𝔽q + u𝔾q + v𝓽q, where q = pm, p is an odd prime and u2 = u,v2 = v,uv = vu = 0, are studied.
Abstract: In this paper, the skew constacyclic codes over finite non-chain ring ℛ = 𝔽q + u𝔽q + v𝔽q, where q = pm, p is an odd prime and u2 = u,v2 = v,uv = vu = 0, are studied. We show that the Gray image of ...

12 citations


Journal ArticleDOI
TL;DR: The concept of neutrosophic implicative in [Formula: see text]-ideal in algebras is introduced, several properties are investigated, and characterizations of the neutrosophile implicative are provided.
Abstract: In the present paper, we introduce the concept of neutrosophic implicative 𝒩-ideal in BCK-algebras, and investigate several properties. Also, we provide characterizations of the neutrosophic implic...

12 citations


Journal ArticleDOI
TL;DR: A k-hop dominating set D of a graph G = (V,E) is a subset of V such that every vertex x ∈ V is within k-steps from at least one vertex y ∈ D, i.e., d(x,y) ≤ k.
Abstract: For a fixed positive integer k, a k-hop dominating set D of a graph G = (V,E) is a subset of V such that every vertex x ∈ V is within k-steps from at least one vertex y ∈ D, i.e., d(x,y) ≤ k. A k-h...

10 citations


Journal ArticleDOI
TL;DR: The well-known Wiener index is defined as the sum of pairwise distances between vertices, and a generalization of the Wiene...
Abstract: The well-known Wiener index is defined as the sum of pairwise distances between vertices. Extremal problems with respect to it have been extensively studied for trees. A generalization of the Wiene...

10 citations


Journal ArticleDOI
TL;DR: It is shown that not every connected, vertex-transitive graph has a Hamilton path, but there is growing interest in solving this longstanding problem and still it remai...
Abstract: Lovasz had posed a question stating whether every connected, vertex-transitive graph has a Hamilton path in 1969. There is a growing interest in solving this longstanding problem and still it remai...

9 citations


Journal ArticleDOI
TL;DR: Consider a simple graph G of order n and size m having Laplacian eigenvalues μ1,μ2,…,μn−1, μn = 0.
Abstract: Consider a simple graph G of order n and size m having Laplacian eigenvalues μ1,μ2,…,μn−1,μn = 0. Let Sk(G) =∑i=1kμ i be the sum of k largest Laplacian eigenvalues of G. Brouwer conjectured that Sk...

8 citations


Journal ArticleDOI
TL;DR: This paper gave a short survey on recent results about strong edge-coloring of a graph.
Abstract: A strong edge-coloring of a graph G = (V,E) is a partition of its edge set E into induced matchings. In this paper, we gave a short survey on recent results about strong edge-coloring of a graph.

7 citations


Journal ArticleDOI
TL;DR: This paper begins an exploration of some of this additional information about phylogeny reconstruction by describing the phylogeny as a Steiner tree within the Cayley graph, and exploring the "interval" between two genomes.
Abstract: Many models of genome rearrangement involve operations that are self-inverse, and hence generate a group acting on the space of genomes. This gives a correspondence between genome arrangements and ...

7 citations


Journal ArticleDOI
TL;DR: A random greedy [Formula: see text]-approximation algorithm and a deterministic[Formula] value oracle queries are proposed in this paper and both algorithms work in value oracles model.
Abstract: We consider the problem of maximizing monotone submodular function over the bounded integer lattice with a cardinality constraint. Function f : ℤ+E → R + is submodular over integer lattice if f(x) ...

7 citations


Journal ArticleDOI
TL;DR: This work studies the expected sum over all sensors i from 1 to n, where the sum is the uniform distribution on the unit interval.
Abstract: Assume that n mobile sensors are thrown uniformly and independently at random with the uniform distribution on the unit interval. We study the expected sum over all sensors i from 1 to n, where the...

Journal ArticleDOI
TL;DR: Some variants of corona of graphs namely, subdivision, neighborhood corona, R-graph (respectively, Q-graph, total) semi-edge neighbor, and subdivision and subdivision of graphs are defined.
Abstract: In this paper, we define some variants of corona of graphs namely, subdivision (respectively, R-graph, Q-graph, total) neighborhood corona, R-graph (respectively, Q-graph, total) semi-edge neighbor...

Journal ArticleDOI
TL;DR: In this paper, the notion of interval-valued intuitionistic fuzzy (IVIF) KU-subalgebras of K U-alge bras are introduced and some fundamental properties are discussed.
Abstract: In this paper, the notion of interval-valued intuitionistic fuzzy (IVIF) KU-subalgebras of KU-algebras are introduced and some fundamental properties are discussed. The image and the inverse image ...

Journal ArticleDOI
TL;DR: For a set W = {s1,s2,…,sk} of vertices of a graph G, the representation multiset of a vertex v of G with respect to W is r(v|W) = d(v,s1), d (v, s2),…,d( v,sk) where d(V,si) is a distance between v and W.
Abstract: For a set W = {s1,s2,…,sk} of vertices of a graph G, the representation multiset of a vertex v of G with respect to W is r(v|W) = {d(v,s1),d(v,s2),…,d(v,sk)}, where d(v,si) is a distance between of...

Journal ArticleDOI
TL;DR: For a group G and a subset X of G, the commuting graph of X, denoted by Γ(X) = ℭ(D(G),X) is the graph whose vertex set is X and any two vertices u and v in X are adjacent if and only if they commut...
Abstract: For a group G and a subset X of G, the commuting graph of X, denoted by Γ(X) = ℭ(D(G),X) is the graph whose vertex set is X and any two vertices u and v in X are adjacent if and only if they commut...

Journal ArticleDOI
TL;DR: The intersection graph of ideals of ℤm, denoted by G(Ωm), is a graph with the vertex set I(™m)∗ and two disti...
Abstract: Let m > 1 be an integer, and let I(ℤm)∗ be the set of all non-zero proper ideals of ℤm. The intersection graph of ideals of ℤm, denoted by G(ℤm), is a graph with the vertex set I(ℤm)∗ and two disti...

Journal ArticleDOI
TL;DR: This paper presents two radio [Formula: see text]-coloring algorithms for general graphs which will produce radio [formula:see text]-colorings with their spans and the time complexity of the both algorithm is of [/Formula]: see text.
Abstract: Due to the rapid growth in the use of wireless communication services and the corresponding scarcity and the high cost of radio spectrum bandwidth, Channel assignment problem (CAP) is becoming high...

Journal ArticleDOI
TL;DR: The log-concavity of a sequence of p,q-binomial coefficients located on a ray of the p-q-Pascal triangle for certain directions is studied and the preserving log- ConcavITY of linear trapezium coefficients is established.
Abstract: We study the log-concavity of a sequence of p,q-binomial coefficients located on a ray of the p,q-Pascal triangle for certain directions, and we establish the preserving log-concavity of linear tra...

Journal ArticleDOI
TL;DR: A Roman dominating function of a graph G is a labeling f : V (G)→{0, 1, 2} such that every vertex with label 0 has a neighbor with label 2.
Abstract: A Roman dominating function of a graph G is a labeling f : V (G)→{0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number, γR(G) of G, is the minimum o...

Journal ArticleDOI
TL;DR: It is shown that the decomposition of a graph G into α,β,γ copies, where α,α,H 2β,H 3γ are non-negative integers, is feasible with respect to discrete numbers.
Abstract: By a {H1α,H 2β,H 3γ}-decomposition of a graph G, we mean a decomposition of G into α copies of H1, β copies of H2 and γ copies of H3, where α,β,γ are non-negative integers. In this paper, it is pro...

Journal ArticleDOI
TL;DR: The conditions for any ℤ2ℤ 2[u]-cyclic code to be self-dual are determined, that is, 𝒞 = 𝓞⊥ since the binar...
Abstract: In this paper, we introduce self-dual cyclic codes over the ring ℤ2 × (ℤ2 + uℤ2) = ℤ2ℤ2[u]. We determine the conditions for any ℤ2ℤ2[u]-cyclic code to be self-dual, that is, 𝒞 = 𝒞⊥. Since the binar...

Journal ArticleDOI
TL;DR: A connected graph with a distance matrix D and the distance signless Laplacian matrix D is a graph with connected components G, where G is the number of connected graphs in the graph.
Abstract: Let G be a connected graph with a distance matrix D. Let DL(G) = Tr(G) − D(G) and DQ(G) = Tr(G) + D(G) be, respectively, the distance Laplacian matrix and the distance signless Laplacian matrix of ...

Journal ArticleDOI
TL;DR: For a molecular graph G, the F-index or forgotten topological index is defined as the sum of cubes of degree of all vertices of the graph and the hyper-Zagreb index is equal to thesum of square of the vertices.
Abstract: For a molecular graph G, the F-index or forgotten topological index is defined as the sum of cubes of degree of all vertices of the graph and the hyper-Zagreb index is equal to the sum of square of...

Journal ArticleDOI
TL;DR: The main purpose of this paper is to determine the graphs with the sixth, seventh and eighth minimal [Formula: see text]-values among all the members of the aforementioned class.
Abstract: The irregularity of a graph G is defined as irr(G) =∑uv∈E(G)|du − dv|, where du denotes the degree of a vertex u ∈ V (G) and E(G) is the edge set of G. From the class of all n-vertex (molecular) tr...

Journal ArticleDOI
TL;DR: The distinguishing number (index) D(G) (D′(G)) of a graph G is the least integer d such that G has a vertex (edge) labeling with d labels that is preserved only by a trivial automorphism as mentioned in this paper.
Abstract: The distinguishing number (index) D(G) (D′(G)) of a graph G is the least integer d such that G has a vertex (edge) labeling with d labels that is preserved only by a trivial automorphism. In this p...

Journal ArticleDOI
TL;DR: Constant dimension subspace codes are subsets of the finite Grassmann Variety that arise as the orbit of subgroup of general linear group acting as a subspace code for constant dimension sub space codes.
Abstract: Constant dimension subspace codes are subsets of the finite Grassmann Variety. Orbit codes are constant dimension subspace codes that arise as the orbit of subgroup of general linear group acting o...

Journal ArticleDOI
TL;DR: The tight bound of the total coloring conjecture for the three types of corona products (vertex, edge and neighborhood) of graphs is proved.
Abstract: A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph G, den...

Journal ArticleDOI
Bandhu Prasad1
TL;DR: A new complex fibonacci matrix Hp,n whose elements are complex Fibonacci numbers and a new coding and decoding method followed from this complex Fib onacci matrix is introduced.
Abstract: In this paper, we introduce a new complex Fibonacci matrix Hp,n whose elements are complex Fibonacci numbers and we developed a new coding and decoding method followed from this complex Fibonacci m...

Journal ArticleDOI
TL;DR: Several inequalities involving the graph invariants [Formula: see text] and [Formulari] are derived and all the bounds established in the aforementioned paper are improved.
Abstract: Let G be a simple graph of order n, without isolated vertices. Denote by A = (aij)n×n the adjacency matrix of G. Eigenvalues of the matrix A, λ1 ≥ λ2 ≥⋯ ≥ λn, form the spectrum of the graph G. An i...

Journal ArticleDOI
TL;DR: In this paper, the number of passes a permutation needs to take through a stack if only pop the appropriate output values and start over with the remaining entries in their original order is considered.
Abstract: We consider the number of passes a permutation needs to take through a stack if we only pop the appropriate output values and start over with the remaining entries in their original order. We defin...