Asian Research Journal of Current Science

Twin Edge Coloring of Product Graphs

J. Naveen *

Department of Mathematics, Government Arts College, Chidambaram, Tamil Nadu, India.

*Author to whom correspondence should be addressed.

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Abstract

A twin edge k-coloring of a graph G is a proper edge k-coloring of G with the elements of Z_k so that the induced vertex k-coloring, in which the color of a vertex v in G is the sum in Z_k of the colors of the edges incident with v is a proper vertex k- coloring. The minimum k for which G has a twin edge k- coloring is called the twin chromatic index of G. Twin chromatic index of the Alternate triangular snake, Triangular snake and Double alternate triangular snake are determined. Twin chromatic index of P_m\(\bullet\)P_m , is also determined, where \(\bullet\) denotes the semi strong product of paths P_m and Pn respectively.

Keywords: Twin edge coloring, twin chromatic index, path, triangular snake, semi strong product

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