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$F$ -continuous graphs

Gary Chartrand; Elzbieta B. Jarrett; Farrokh Saba; Ebrahim Salehi; Ping 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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F -continuous graphs

$F$ -continuous graphs