منابع مشابه
Group connectivity in line graphs
Tutte introduced the theory of nowhere zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere zero A-flow, for any Abelian group A with |A| ≥ k. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientationD of a graph G, if for any b : V (G) → Awith v∈V (G) b(v) = 0, there always exists a map f : E(G) →...
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The super connectivity κ ′ and the super edge-connectivity λ′ are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ ′(L(G))= λ′(G) if and only if G is not super-λ′. As a consequence, we obtain the result of Hellwig et al. [Note on the connectiv...
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متن کاملGroup Connectivity of Kneser Graphs
Let G be an undirected graph, A be an (additive) abelian group and A∗ = A−{0}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V (G) → A satisfying ∑v∈V (G) b(v) = 0, there is a function f : E(G) → A∗ such that ∑e∈E+(v) f(e) − ∑ e∈E−(v) f(e) = b(v). For an abelian group A, let 〈A〉 be the family of graphs that are A-connected. The group connectivity number ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.07.017