Eigenvalues of Status Sum Adjacency Matrix of Graphs

S.Y. Talwar¹ , H.S. Ramane²

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.4 , pp.67-69, Aug-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i4.6769

Online published on Aug 31, 2019

Copyright © S.Y. Talwar, H.S. Ramane . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The distance between two vertices is the length of a shortest path joining them. The status (u) of vertex u in a connected graph G is defined as sum of distances between u and all other vertices in graph G. The status sum adjacency matrix of a graph G is SA(G) = [sij] in which sij = (u) + (v) if u and v are adjacent vertices and sij = 0, otherwise. In this paper we initiate the study of eigenvalues of status sum adjacency matrix of graphs.

Key-Words / Index Term :
Distance in graphs, status of a vertex, status sum adjacency matrix, eigenvalues

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