Results 31 to 40 of about 50 (50)
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SIAM Journal on Discrete Mathematics, 2002
For a nonnegative weight function \(\pi\) on vertices \(u\) of a finite connected graph \(G\), let \[ F_{\pi} (x)=\sum_u \pi(u) d(u,x) \] where \(d\) denotes the distance. The median set consists of all vertices \(x\) which give a minimum of \(F_{\pi} (x)\).
Hans-Jürgen Bandelt, Victor Chepoi
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For a nonnegative weight function \(\pi\) on vertices \(u\) of a finite connected graph \(G\), let \[ F_{\pi} (x)=\sum_u \pi(u) d(u,x) \] where \(d\) denotes the distance. The median set consists of all vertices \(x\) which give a minimum of \(F_{\pi} (x)\).
Hans-Jürgen Bandelt, Victor Chepoi
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On hamiltonian‐connected graphs
Journal of Graph Theory, 1994AbstractOne of the most fundamental results concerning paths in graphs is due to Ore: In a graph G, if deg x + deg y ≧ |V(G)| + 1 for all pairs of nonadjacent vertices x, y ≅ V(G), then G is hamiltonian‐connected. We generalize this result using set degrees.
Ronald J. Gould, Xingxing Yu
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On Group Connectivity of Graphs
Graphs and Combinatorics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hong-Jian Lai, Rui Xu 0023, Ju Zhou
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The Connectivity of Token Graphs
Graphs and Combinatorics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jesús Leaños +1 more
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On thel-connectivity of a graph
Graphs and Combinatorics, 1987Let be \(\ell \geq 2\), then the \(\ell\)-connectivity of a graph G, \(\kappa_{\ell}(G)\), in the minimum number of vertices whose removal produces a disconnected graph with at least \(\ell\) components or a graph with fewer than \(\ell\) vertices. A graph is said to be (n,\(\ell)\)- connected if \(\kappa_{\ell}(G)\geq n\). \textit{G. Chartrand, S.
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Spanning Connectivity of the Power of a Graph and Hamilton-Connected Index of a Graph
Graphs and Combinatorics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eminjan Sabir, Elkin Vumar
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2001
A join in a graph is a set F of edges such that for every circuit C, |C ∩ F| ≤ |C \ F|. We study the problem of finding a connected join covering a given subset of vertices of the graph, that is a Steiner tree which is a join at the same time. This turns out to contain the question of finding a T-join of minimum cardinality (or weight) which is, in ...
Sebő, András, Tannier, Eric
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A join in a graph is a set F of edges such that for every circuit C, |C ∩ F| ≤ |C \ F|. We study the problem of finding a connected join covering a given subset of vertices of the graph, that is a Steiner tree which is a join at the same time. This turns out to contain the question of finding a T-join of minimum cardinality (or weight) which is, in ...
Sebő, András, Tannier, Eric
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Connectivity and Reducibility of Graphs
Canadian Journal of Mathematics, 1962Corresponding to every graph, bipartite graph, or directed bipartite graph there exists a directed graph which is connected if and only if the original graph is connected.In this paper, it is shown that for every directed graph there exists a certain bipartite graph such that the directed graph is connected if and only if the bipartite graph is ...
Johnson, Diane M. +2 more
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The rainbow connectivity of a graph
Networks, 2009AbstractA path P in an edge‐colored graph (not necessarily a proper edge‐coloring) is a rainbow path if no two edges of P are colored the same. For an ℓ‐connected graph G and an integer k with 1 ≤ k ≤ ℓ, the rainbow k‐connectivity rck(G) of G is the minimum integer j for which there exists a j‐edge‐coloring of G such that every two distinct vertices of
Gary Chartrand +3 more
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The chromatic connectivity of graphs
Graphs and Combinatorics, 1988A graph G is chromatically k-connected iff every vertex-cutset induces a subgraph of G with chromatic number at least k. The authors prove that each planar \(K_ 4\)-free graph is at most chromatically 2-connected and show that a \(K_ 5\)-free graph which can be embedded on the torus is at most chromatically 3-connected.
Chris D. Godsil +2 more
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