On star coloring of modular product of graphs

Yıl 2020, Cilt: 69 Sayı: 2, 1235 - 1239, 31.12.2020

Kaliraj K Sivakami R Vernold Vıvın J

https://doi.org/10.31801/cfsuasmas.768497

Cited By: 1

Öz

A star coloring of a graph $G$ is a proper vertex coloring in which every path on four vertices in $G$ is not bicolored. The star chromatic number $\chi_{s}\left(G\right)$ of $G$ is the least number of colors needed to star color $G$. In this paper, we find the exact values of the star chromatic number of modular product of complete graph with complete graph $K_m \diamond K_n$, path with complete graph $P_m \diamond K_n$ and star graph with complete graph $K_{1,m}\diamond K_n$.

\par All graphs in this paper are finite, simple, connected and undirected graph and we follow \cite{bm, cla, f} for terminology and notation that are not defined here. We denote the vertex set and the edge set of $G$ by $V(G)$ and $E(G)$, respectively. Branko Gr\"{u}nbaum introduced the concept of star chromatic number in 1973. A star coloring \cite{alberton, fertin, bg} of a graph $G$ is a proper vertex coloring in which every path on four vertices uses at least three distinct colors. The star chromatic number $\chi_{s}\left(G\right)$ of $G$ is the least number of colors needed to star color $G$.

\par During the years star coloring of graphs has been studied extensively by several authors, for instance see \cite{alberton, col, fertin}.

Anahtar Kelimeler

Star Coloring, Modular Product, Star graph

Kaynakça

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