Extremal Properties of Kirchhoff Index and Degree Resistance Distance of Unicyclic Graphs

Let G be a connected graph with vertex set V(G). The Kirchhoff index of G is defined as K f( G) = Sigma({u,v}subset of V(G)) R(u, v vertical bar G), and the degree resistance distance of G is defined as D-R(G) = Sigma{u,v}subset of V(G) [d(u vertical bar G) + d(V vertical bar G)]R(U, v vertical bar G) , where R(u, v vertical bar G) denotes the resistance distance between vertices u and v in G, and d(u vertical bar G) denotes the degree of the vertex u in G. In this paper, we mainly determine maximum Kirchhoff index and maximum degree resistance distance of n-vertex unicyclic graphs with given maximum degree, and characterize their extremal graphs. In addition, maximum Kirchhoff index and maximum degree resistance distance of n-vertex unicyclic graphs can be determined as corollaries, which are results in [3,24,26].