Abstract

Equitable Total Coloring of Direct Product of Path and Cycle

S. Moidheen Aliyar1*, S. Manimaran2 and K. Manikandan3

1*Department of Mathematics, The New College, Chennai-600 014, Tamilnadu, INDIA. 2Department of Mathematics, RKM Vivekanandha College, Chennai-600 004, Tamilnadu, INDIA. 3Department of Mathematics, Guru Nanak College, Chennai-600 042, Tamilnadu, INDIA.

DOI : http://dx.doi.org/10.29055/jcms/1137

ABSTRACT

An equitable total coloring of graph 𝐺 is an assignment of colors to all the elements (vertices, edges) of graph 𝐺 such that adjacent or incident elements receive the different color and for any two color classes different by at most one. In this paper, we obtain the exact expressions for the equitable total coloring of direct product of path and cycle. Mathematics Subject Classification: 05C15.

Keywords :Equitable total coloring, Tensor product, Direct product and cycle graph.

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