Extremal cacti of given matching number with respect to the distance spectral radius

摘要

A cactus is a connected graph in which any two cycles have at most one common vertex. The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Recently, many researchers proposed the use of ρ(G) as a molecular structure descriptor of alkanes. In this paper, we characterize n-vertex cyclic cactus with given matching number m which minimizes the distance spectral radius. The resulting cactus also minimizes the Hosoya index, the Wiener index and the Randić index in the same class of graphs.