On the Spectra of Reduced Distance Matrix of Thorn Graphs

Document Type : Research Paper


Arak Branch, Islamic Azad University, Arak, Iran


Let G be a simple connected graph and {v1, v2, …, vk} 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 vi and vj of G. In this paper, we obtain the spectrum of the reduced distance matrix of thorn graph of G, a graph which obtained by attaching some new vertices to pendent vertices of G. As an application we compute the spectrum of reduced distance matrix for some dendrimer graphs.