On the spectra of reduced distance matrix of dendrimers

Abstract

Let $G$ be a simple connected graph and ${v_1,v_2,ldots‎, ‎v_k}$ be the set of‎ ‎pendent (vertices of degree one) vertices of $G$‎. ‎The reduced distance matrix of $G$ is a square matrix whose $(i,j)$-entry is the topological distance between $v_i$ and $v_j$ of $G$‎. ‎In this paper‎, ‎we obtain the spectrum‎ ‎of the reduced distance matrix of regular dendrimers‎.