Results 1 to 10 of about 50 (50)
Vector Connectivity in Graphs [PDF]
Networks, 2013 AbstractMotivated by challenges related to domination, connectivity, and information propagation in social and other networks, we initiate the study of the VECTOR CONNECTIVITY problem. This problem takes as input a graph G and an integer kv for every vertex v of G, and the objective is to find a vertex subset S of minimum cardinality such that every ...
Endre Boros +3 more
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The Orderings of Bicyclic Graphs and Connected Graphs by Algebraic Connectivity [PDF]
The Electronic Journal of Combinatorics, 2010 The algebraic connectivity of a graph $G$ is the second smallest eigenvalue of its Laplacian matrix. Let $\mathscr{B}_n$ be the set of all bicyclic graphs of order $n$. In this paper, we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in $\mathscr{B}_n$ when $n\geq 13$.
Jianxi Li, Ji-Ming Guo, Wai Chee Shiu
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The Connectivities of Leaf Graphs of 2-Connected Graphs
Journal of Combinatorial Theory, Series B, 1999 Given a connected graph \(G=(V,E)\), its leaf graph \(\mathcal G\) has as vertex set the set of all spanning trees of \(G\); two vertices \(S\) and \(T\) of \(\mathcal G\) are adjacent exactly when there exists \(v\in V\) such that \(S-v=T-v\) is a connected subgraph of \(G\).
Atsushi Kaneko, Kiyoshi Yoshimoto
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On the Connectivity of Visibility Graphs [PDF]
Discrete & Computational Geometry, 2012 16 pages, 8 ...
Michael S. Payne +3 more
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Connectivity of Planar Graphs [PDF]
Journal of Graph Algorithms and Applications, 2001 We give here three simple linear time algorithms on planar graphs: a 4-connexity test for maximal planar graphs, an algorithm enumerating the triangles and a 3-connexity test. Although all these problems got already linear-time solutions, the presented algorithms are both simple and efficient. They are based on some new theoretical results.
de Fraysseix, Hubert +1 more
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Rainbow Connection in 3-Connected Graphs [PDF]
Graphs and Combinatorics, 2012 An edge-colored graph $G$ is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph $G$, denoted by $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected.
Xueliang Li 0001, Yongtang Shi
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Coloring Graphs with Constraints on Connectivity [PDF]
Journal of Graph Theory, 2016 AbstractA graph G has maximal local edge‐connectivity k if the maximum number of edge‐disjoint paths between every pair of distinct vertices x and y is at most k. We prove Brooks‐type theorems for k‐connected graphs with maximal local edge‐connectivity k, and for any graph with maximal local edge‐connectivity 3.
Aboulker, Pierre +4 more
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THE MAXIMUM CONNECTIVITY OF A GRAPH [PDF]
Proceedings of the National Academy of Sciences, 1962 Abstract : The paper solves the problem of the maximum connectivity of any graph with a given number of points and lines. In addition, the minimum connectivity. The maximum diameter, and the minimum diameter are obtained. Two unsolved problems concerning the distribution of the values of the connectivity and the diameter are included.
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Information and Computation, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barrière, Lali +6 more
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A Partition of Connected Graphs
The Electronic Journal of Combinatorics, 2005 We define an algorithm $k$ which takes a connected graph $G$ on a totally ordered vertex set and returns an increasing tree $R$ (which is not necessarily a subtree of $G$). We characterize the set of graphs $G$ such that $k(G)=R$. Because this set has a simple structure (it is isomorphic to a product of non-empty power sets), it is easy to evaluate ...
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