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F -continuous graphs

Gary ChartrandElzbieta B. JarrettFarrokh SabaEbrahim SalehiPing Zhang — 2001

Czechoslovak Mathematical Journal

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, there...

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