Degree tolerant coloring: Graphs from graphs

Abstract

Degree tolerant coloring is a study on a new coloring regime which sets conditions in respect of $\operatorname{deg}(v)$ and $\operatorname{deg}(u)$ where, $v, u \in V(G)$ and $v u \in E(G)$. Results for graphs from graphs or (derivative graphs) such the line graph, the middle graph, the total graph, the power graph and others, are presented in this paper.