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Spectral Properties with the Difference between Topological Indices in Graphs

Author

Listed:
  • Akbar Jahanbani
  • Roslan Hasni
  • Zhibin Du
  • Seyed Mahmoud Sheikholeslami
  • Li Guo

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.

Suggested Citation

  • Akbar Jahanbani & Roslan Hasni & Zhibin Du & Seyed Mahmoud Sheikholeslami & Li Guo, 2020. "Spectral Properties with the Difference between Topological Indices in Graphs," Journal of Mathematics, Hindawi, vol. 2020, pages 1-10, July.
    • Handle: RePEc:hin:jjmath:6973078
    DOI: 10.1155/2020/6973078
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