SPN-Matrix Completion Problem for Star Bi-directed Graph

Abstract

In this paper an SPN-Matrix is considered. A Vertex distance path matrix (V_Dp) representing theStar bi-directed graph S_n is said to have an SPN-completion if every partial SPN-matrix specifying V_Dp can be completed to anSPN-Matrix. It is shown that the SPN-matrices representing all Star bi-directed graphs S_nof n vertices and 2(n-1) edges have an SPN-matrix completion. In addition a study on another distance matrix related to the q distance matrix andthe exponential distance matrix of a tree thathave an SPN–matrix completion is also characterized.