On dynamic coloring of certain cycle-related graphs

Arabian Journal of Mathematics, Aug 2018

Coloring the vertices of a particular graph has often been motivated by its utility to various applied fields and its mathematical interest. A dynamic coloring of a graph G is a proper coloring of the vertex set V(G) such that for each vertex of degree at least 2, its neighbors receive at least two distinct colors. A dynamic k-coloring of a graph is a dynamic coloring with k colors. A dynamic k-coloring is also called a conditional (k, 2)-coloring. The smallest integer k such that G has a dynamic k-coloring is called the dynamic chromatic number $$\chi _d(G)$$ of G. In this paper, we investigate the dynamic chromatic number for the line graph of sunlet graph and middle graph, total graph and central graph of sunlet graphs, paths and cycles. Also, we find the dynamic chromatic number for Mycielskian of paths and cycles and the join graph of paths and cycles. Open image in new window

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J. Vernold Vivin, N. Mohanapriya, Johan Kok, M. Venkatachalam. On dynamic coloring of certain cycle-related graphs, Arabian Journal of Mathematics, 2018, 1-9, DOI: 10.1007/s40065-018-0219-3