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    On optimal vertex colorings of graphs
    (Maltepe Üniversitesi, 2009) Parsa, Esmaeil
    Let c be a k-coloring of a graph G, then the number of different colors which appear in N(v) is called the coloring degree of v with respect to c and denoted by Cdc(v). K-coloring index of G is denoted by Cik(G) and defined as Cik(G) = M in{ P v?V (G) Cdc(v)} which, the minimum is over all k-colorings of G. A coloring c is called an optimal coloring of G if P v?V (G) cdc(v) 6 Cik(G), ?k. In this paper we provide some essential conditions for coloring c to be an optimal coloring and provide an algorithm to create an optimal coloring of a graph G as a conjecture along with some open problems.