2015/11/15 by Liu, Jia-Bao, Pan, Xiang-Feng
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1511.04704
Various topological indices, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph G is defined as DR(G) = ∑_\u,v\ ⊆ V(G) [d(u) + d(v)]R(u,v), where d(u) is the degree of the vertex u, and R(u, v) the resistance distance between the vertices u and v. A graph G is called a cactus if each block of G is either an edge or a cycle. In this paper, we completely characterize the extremal cacti having the maximum degree resistance distance among all cacti with n vertices and t cycles, and extend some results of a recent paper [J. Tu, J. Du, G. Su, The unicyclic graphs with maximum degree resistance distance, Appl. Math. Comput. 268 (2015) 859-864].