On the r-dynamic coloring of some fan graph families

Abstract

In this paper, we determine the r-dynamic chromatic number of the fan graph Fm,n and determine sharp bounds of this graph invariant for four related families of graphs: The middle graph M(Fm,n), the total graph T (Fm,n), the central graph C(Fm,n) and the line graph L(Fm,n). In addition, we determine the r-dynamic chromatic number of each one of these four families of graphs in case of being m = 1.