Abstract

The Sigma coloring of a graph $G$ is an assignment of natural numbers to the vertices of $G$ such that the color sums (the sum of the colors of the adjacent vertices) of any two adjacent vertices are different. The Sigma Chromatic number of a graph $G$, $\sigma(G)$, is the least number of colors used in a sigma coloring of $G$. In this paper, we investigate the sigma coloring and Sigma Chromatic number of some graph operations such as Tensor product of graphs, Ring sum of graphs and Joint-sum of graphs. We also obtain the sigma coloring and Sigma Chromatic number of some special graphs such as the graphs obtained by duplicating an arbitrary vertex and an arbitrary edge in cycle graphs, $C_n$, fusion of two vertices in cycle graphs, $C_n$, two copies of cycle graphs sharing a common edge.

Keywords and Phrases

$\sigma-$coloring, Sigma Chromatic number, Tensor-Product, Ring-Sum, Joint-Sum.

A.M.S. subject classification

05C15.

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