On the degree Kirchhoff index of unicyclic graphs

Let G be a connected graph with vertex set V(G). The degree Kirchhoff index of G is defined as Kf*(G) = Sigma({u,v}subset of V(G)) d(G)(u)d(G)(v)R-G(u, v), where d(G)(u) denotes the degree of the vertex u in G, and R-G(u, v) denotes the resistance distance between vertices u and v in G. In this paper, we determine maximum degree Kirchhoff index of n-vertex unicyclic graphs with fixed maximum degree, the first seven maximum degree Kirchhoff indices of n-vertex unicyclic graphs, and the corresponding graphs whose degree Kirchhoff indices achieve these values. (C) 2020 Published by Elsevier B.V.