Twin Edge Coloring of Some Path and Cycle Related Graphs: A Recent Study

A valid edge K-coloring of G with the elements of Zk is a twin edge K-coloring of a graph, therefore the induced vertexK-coloring is a proper vertexK-coloring, in which the colour of a vertex V in G is the sum in Zk of the colours of the edges interacting with v. The twin chromatic index of G is the lowest K for which G has a twin edge K-coloring. The splitting graph of path and cycle, middle graph of path and cycle, and shadow graph of path and cycle all have twin chromatic indexes. The twin chromatic index of Cm X Pn, where X indicates the direct product of Cr and Pr, is also computed. The cycle and the route on each of the r vertices.

Author(s) Details:

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

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