1Assistant Professor, Department of Mathematics, Srimed Andavan Arts & Science College, Trichy-05, Tamilnadu, India, E-mail: ponmudims@gmail.com
2Assistant Professor, Department of Mathematics, Srimed Andavan Arts & Science College, Trichy-05, Tamilnadu, India, E-mail: andavanmathsramesh@gmail.com
*Corresponding Author: A. Rameshkumar, Assistant Professor & Research Adviser, Department of Mathematics, Srimad Andavan Arts and Science College (Autonomous) No.7, Nelson Road, T.V. Kovil, Trichy-05, Tamilnadu, India, E-mail: andavanmathsramesh@gmail.com
AMS Mathematics Subject Classification: 15A 18, 15A57
In this paper an SPN-Matrix is considered. A Vertex distance path matrix (VDp) representing the Star bidirected graph Sn is said to have an SPN-completion if every partial SPN-matrix specifying VDp can be completed to an SPN-Matrix. It is shown that the SPN-matrices representing all Star bi-directed graphs Snof 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.
Bi-directed Star graph, vertex distance path matrix, distance matrix, SPN-completion
