On colorings of strongly multiplicative and strongly quotient graphs
Chandrashekara Adiga, R. K. Zaferani · Advanced Studies in Contemporary Mathematics · 2006
Review : A graph $G$ of order $n$ is called strongly multiplicative (strongly quotient) if there is an injection $f$ from the set of vertices of $G$ to $\{1,2,\dots,n\}$ such that the edge labels induced by $f(u)f(v)$ (by $\min\{f(u),f(v)\}/\max\{f(u),f(v)\}$) for each edge $uv$ are distinct. In the paper the authors establish some bounds for the chromatic number of strongly multiplicative graphs. They also investigate the chromatic number, the clique number, the independence number and the cardinality of a minimum defining set of some strongly quotient graphs.