Spectral Properties with the Difference between Topological Indices in Graphs

Akbar Jahanbani, Roslan Hasni, Zhibin Du, Seyed Mahmoud Sheikholeslami and Li Guo

Journal of Mathematics, 2020, vol. 2020, 1-10

Abstract: Let G be a graph of order n with vertices labeled as v1,v2,…,vn. Let di be the degree of the vertex vi, for i=1,2,…,n. The difference adjacency matrix of G is the square matrix of order n whose i,j entry is equal to di+dj−2−1/didj if the vertices vi and vj of G are adjacent or vivj∈EG and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6973078

DOI: 10.1155/2020/6973078

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