Results 21 to 30 of about 50 (50)

On spanning connected graphs

Discrete Mathematics, 2008
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Cheng-Kuan Lin, Hua-Min Huang, Jimmy J. M. Tan, Lih-Hsing Hsu   +3 more
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Connectivity of distance graphs

Discrete Mathematics, 1992
Let \(K\supseteq\mathbb{Q}\) be a \(\mathbb{Z}\)-module and \(G\) a graph with a \(K\)- space as vertex set \(V\). If the edges of \(G\) are preserved under translations in \(V\) and \(G\) has more than one connected component, then the author shows that \(G\) has infinitely many components.
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The connectivity dimension of a graph

CoRR
This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph. We fully characterize extremal examples and present explicit constructions of infinitely many graphs realizing any
Kurt Klement Gottwald, Tobias Hofmann
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On local connectivity of graphs

Applied Mathematics Letters, 2008
The local connectivity \(k(u,v)\) between two distinct vertices \(u\) and \(v\) of a graph \(G\) is the maximum number of internally disjoint paths between \(u\) and \(v\) in \(G\). Let \(d(x)\) be the degree of a vertex \(x\). A graph \(G\) is maximally locally connected when \(k(u,v) = \min(d(u), d(v))\) for all pairs of \(u\) and \(v\) in \(G\). The
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Path-connectivity in graphs

Discrete Mathematics, 1986
Der Autor nennt einen Graphen \(G(k,n)\)-wegzusammenhängend, wenn es zu jeder \(k\)-elementigen Eckenmenge \(A\) von \(G\) \(n\) kantendisjunkte Wege in \(G\) gibt, die paarweise genau die Ecken von \(A\) gemeinsam haben. Als Hauptergebnis wird gezeigt, daß jeder \((2^{k-2}\cdot n)\)-fach zusammenhängende Graph \((k,n)\)-wegzusammenhängend ist.
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Complexes of Connected Graphs [PDF]

, 1993
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory, combinatorics, and singularity theory. The multidimensional analogues of this complex are indicated, which arise naturally
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On the tree graph of a connected graph

Discussiones Mathematicae Graph Theory, 2008
Ana Paulina Figueroa, Eduardo Rivera-Campo   +1 more
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Connected Soft Graph

New Mathematics and Natural Computation, 2020
The theory of soft set offers a mathematical tool to deal with uncertainty. Nowadays, work on soft graph theory is progressing rapidly. In this paper, we define connected soft graph and derive some results. We also define cut vertex and bridge of soft graph along with some results on it.
Jyoti D. Thenge, B. Surendranath Reddy, Rupali S. Jain   +2 more
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Graphs with prescribed connectivity and line graph connectivity

Journal of Graph Theory, 1979
AbstractChartrand and Stewart have shown that the line graph of an n‐connected graph is itself n‐connected. This paper shows that for every pair of integers m > n > 1 there is a graph of point connectivity n whose line graph has point connectivity m. The corresponding question for line connectivity is also resolved.
Douglas Bauer, Ralph Tindell
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On Tree-Connectivity and Path-Connectivity of Graphs

Graphs and Combinatorics, 2021
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Shasha Li, Zhongmei Qin, Jianhua Tu, Jun Yue   +3 more
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