On r-dynamic coloring on Mycielskian graphs
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Mycielski graphs are based on transformation from a graph G to a new graph, say μ(G). It is well known that these graphs have same clique number as in the graph G, but the chromatic number is defined as χ(μ(G))=χ(G)+1. The Mycielskian graph G is denoted as μ(G). These Mycielski graphs are colored using r- dynamic coloring which is an proper vertex k-coloring and defined as |c(Neigh(v))|≥min {r, degG(v)}, for each v∈V(G). It is denoted by χr(G). The r-dynamic chormatic number of a graph G is the minutest coloring k of G which is r-dynamic k-colorable. In this paper, the authors investigated the r-coloring of Mycielskian graph of Double Fan graph μ(F2,n), Friendship graph μ(Fn), Pan graph μ(Pn) and Cocktail party graph μ(CPn).
Abstract
Mycielski graphs are based on transformation from a graph G to a new graph, say μ(G). It is well known that these graphs have same clique number as in the graph G, but the chromatic number is defined as χ(μ(G))=χ(G)+1. The Mycielskian graph G is denoted as μ(G). These Mycielski graphs are colored using r- dynamic coloring which is an proper vertex k-coloring and defined as |c(Neigh(v))|≥min {r, degG(v)}, for each v∈V(G). It is denoted by χr(G). The r-dynamic chormatic number of a graph G is the minutest coloring k of G which is r-dynamic k-colorable. In this paper, the authors investigated the r-coloring of Mycielskian graph of Double Fan graph μ(F2,n), Friendship graph μ(Fn), Pan graph μ(Pn) and Cocktail party graph μ(CPn).
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