Displaying similar documents to “Results on F -continuous graphs”

F -continuous graphs

Gary Chartrand, Elzbieta B. Jarrett, Farrokh Saba, Ebrahim Salehi, Ping Zhang (2001)

Czechoslovak Mathematical Journal

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For a nontrivial connected graph F , the F -degree of a vertex v in a graph G is the number of copies of F in G containing v . A graph G is F -continuous (or F -degree continuous) if the F -degrees of every two adjacent vertices of G differ by at most 1. All P 3 -continuous graphs are determined. It is observed that if G is a nontrivial connected graph that is F -continuous for all nontrivial connected graphs F , then either G is regular or G is a path. In the case of a 2-connected graph F , however,...

Degree-continuous graphs

John Gimbel, Ping Zhang (2001)

Czechoslovak Mathematical Journal

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A graph G is degree-continuous if the degrees of every two adjacent vertices of G differ by at most 1. A finite nonempty set S of integers is convex if k ∈ S for every integer k with min ( S ) ≤ k ≤ max ( S ) . It is shown that for all integers r > 0 and s ≥ 0 and a convex set S with min ( S ) = r and max ( S ) = r + s , there exists a connected degree-continuous graph G with the degree set S and diameter 2 s + 2 . The minimum order of a degree-continuous graph with a prescribed degree set is studied. Furthermore, it is shown that for every graph G and convex...

Join of two graphs admits a nowhere-zero 3 -flow

Saieed Akbari, Maryam Aliakbarpour, Naryam Ghanbari, Emisa Nategh, Hossein Shahmohamad (2014)

Czechoslovak Mathematical Journal

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Let G be a graph, and λ the smallest integer for which G has a nowhere-zero λ -flow, i.e., an integer λ for which G admits a nowhere-zero λ -flow, but it does not admit a ( λ - 1 ) -flow. We denote the minimum flow number of G by Λ ( G ) . In this paper we show that if G and H are two arbitrary graphs and G has no isolated vertex, then Λ ( G ∨ H ) ≤ 3 except two cases: (i) One of the graphs G and H is K 2 and the other is 1 -regular. (ii) H = K 1 and G is a graph with at least one isolated vertex or a component whose every...