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Connectivity
About: Connectivity is a research topic. Over the lifetime, 5418 publications have been published within this topic receiving 108611 citations.
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TL;DR: A new type of network growth rule is studied, which comprises nodes adding, plus a rewiring procedure, and replacing of nodes with the complete bipartite graph K 2 , 3 acting on Petersen graph, which has 0 clustering coefficient, short diameter, high connectivity and the Hamilton path.
03 Feb 2018
TL;DR: The relation between the maximal ideal of a commutative ring and the thenumber of partite of a graph G(R)4(R), where R denotes the Jacobson radical of R, is studied in this article.
Abstract: Let R be a commutative ring and G(R) be a graph with vertices as proper andnon-trivial ideals of R Two distinct vertices I and J are said to be adjacentif and only if I + J = R In this paper we study a graph constructed froma subgraph G(R)Δ(R) of G(R) which consists of all ideals I of R such thatI Δ J(R), where J(R) denotes the Jacobson radical of R In this paper westudy about the relation between the number of maximal ideal of R and thenumber of partite of graph G(R)4(R) Also we study on the structure of ringR by some properties of vertices of subgraph G(R)4(R) In another section,it is shown that under some conditions on the G(R), the ring R is Noetherianor Artinian Finally we characterize clean rings and then study on diameterof this constructed graph
TL;DR: In this article, it was shown that if G is a simple graph and G σ is an oriented graph of G with skew adjacency matrix S (G σ ), then the skew spectral radius ρ s (G ) is the same for all orientations σ of G, must G be an odd-cycle graph?
TL;DR: This paper focuses on the labeling schemes that not only enable a robot to explore the graph but also allow the system designer to adjust the ratio of the number of different labels, necessary when maintaining different labels may have different costs or when the ratio is pre-specified.
Abstract: The graph exploration problem is to visit all the nodes of a connected graph by a mobile entity, e.g., a robot. The robot has no a priori knowledge of the topology of the graph or of its size. Cohen et al. [3] introduced label guided graph exploration which allows the system designer to add short labels to the graph nodes in a preprocessing stage; these labels can guide the robot in the exploration of the graph. In this paper, we address the problem of adjustable 1-bit label guided graph exploration. We focus on the labeling schemes that not only enable a robot to explore the graph but also allow the system designer to adjust the ratio of the number of different labels. This flexibility is necessary when maintaining different labels may have different costs or when the ratio is pre-specified. We present 1-bit labeling (two colors, namely black and white) schemes for this problem along with a labeling algorithm for generating the required labels. Given an n-node graph and a rational number ρ, we can design a 1-bit labeling scheme such that n/b ≥ ρ where b is the number of nodes labeled black. The robot uses O(ρ log Δ) bits of memory for exploring all graphs of maximum degree Δ. The exploration is completed in time . Moreover, our labeling scheme can work on graphs containing loops and multiple edges, while that of Cohen et al. focuses on simple graphs.
07 Dec 2012
TL;DR: This paper has improved the KL clustering with sparse graphs constructed by b-matching method and sparse representation, which has more attractive properties than the classic KL clusters.
Abstract: KL (K-means-Laplacian) clustering combines K-means and spectral clustering algorithm together to use both of the attribute values of data and the pairwise relations between the data points. However, a full connected graph used in KL clustering may not be appropriate to indicate the similarity relations between the data points. This paper has improved the KL clustering with sparse graphs constructed by b-matching method and sparse representation. The b-matching graph, in which each node has strictly b neighbors, is more regular than KNN (K nearest neighbors) graph. Graph constructed by sparse representation (l1 graph) also has many merits such as sparsity and datum-adaptive neighborhoods. Hence the improved KL clustering with the constructed graphs has more attractive properties than the classic KL clustering. The experiments on the benchmark datasets (COIL-20 and MNIST) show the effectiveness of the improved KL clustering with promising results.