On r- dynamic coloring of the family of bistar graphs

Abstract

An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that jc(N (v))j min fr; d(v)g, for each v 2 V (G). The rdynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper, we obtain the r-dynamic chromatic number of middle, total, central and line graph of Bistar graph.

On the r-dynamic coloring of some fan graph families

“…In the recent literature, one can find studies concerning different proper colorings of middle, total, central and line graphs of different types of graphs [5,27,28,30,31]. More specifically, the r-dynamic proper coloring of these four families of graphs has already been studied for bistar graphs [25], gear graphs [7] and helm graphs [10]. Some partial results concerning fan graphs F 1,n may be found in [23].…”