Displaying similar documents to “Degree-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,...

Results on F -continuous graphs

Anna Draganova (2009)

Czechoslovak Mathematical Journal

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For any nontrivial connected graph F and any graph G , the of a vertex v in G is the number of copies of F in G containing v . G is called if and only if the F -degrees of any two adjacent vertices in G differ by at most 1; G is if the F -degrees of all vertices in G are the same. This paper classifies all P 4 -continuous graphs with girth greater than 3. We show that for any nontrivial connected graph F other than the star K 1 , k , k ≥ 1 , there exists a regular graph that is not F -continuous. If...

A note on the independent domination number of subset graph

Xue-Gang Chen, De-xiang Ma, Hua Ming Xing, Liang Sun (2005)

Czechoslovak Mathematical Journal

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The independent domination number i ( G ) (independent number β ( G ) ) is the minimum (maximum) cardinality among all maximal independent sets of G . Haviland (1995) conjectured that any connected regular graph G of order n and degree δ ≤ 1 2 n satisfies i ( G ) ≤ ⌈ 2 n 3 δ ⌉ 1 2 δ . For 1 ≤ k ≤ l ≤ m , the subset graph S m ( k , l ) is the bipartite graph whose vertices are the k - and l -subsets of an m element ground set where two vertices are adjacent if and only if one subset is contained in the other. In this paper, we give a sharp upper bound for i ( S m ( k , l ) ) and...