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On the spectral radius and energy of the weighted adjacency matrix of a graph

Author

Listed:
  • Xu, Baogen
  • Li, Shuchao
  • Yu, Rong
  • Zhao, Qin

Abstract

Let G be a graph of order n and let di be the degree of the vertex vi in G for i=1,2,…,n. The weighted adjacency matrix Adb of G is defined so that its (i, j)-entry is equal to di+djdidj if the vertices vi and vj are adjacent, and 0 otherwise. The spectral radius ϱ1 and the energy Edb of the Adb-matrix are examined. Lower and upper bounds on ϱ1 and Edb are obtained, and the respective extremal graphs are characterized.

Suggested Citation

  • Xu, Baogen & Li, Shuchao & Yu, Rong & Zhao, Qin, 2019. "On the spectral radius and energy of the weighted adjacency matrix of a graph," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 156-163.
    • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:156-163
    DOI: 10.1016/j.amc.2018.08.012
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    References listed on IDEAS

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    1. Das, Kinkar Ch. & Gutman, Ivan & Furtula, Boris, 2017. "On spectral radius and energy of extended adjacency matrix of graphs," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 116-123.
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