DP-coloring as a generalization of list coloring was introduced recently by Dvorak and Postle. The DP-chromatic number of G, denoted by chi(DP)(G), is the minimum number k such that G is DP - k-colorable. The variation of the Randic index R'(G) of a graph G is defined as the sum of the weights 1/max{d(u),d(v)} of all edges u(v) of G, where d(u) is the degree of the vertex u in G. In this paper, we show that for any graph G of order n, X-DP(G) <= 2R'(G), and this bound is sharp for all n and 2 <= chi(DP)(G) <= n. (C) 2022 Elsevier B.V. All rights reserved.
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