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On spectral radius and energy of extended adjacency matrix of graphs

Author

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  • Das, Kinkar Ch.
  • Gutman, Ivan
  • Furtula, Boris

Abstract

Let G be a graph of order n. For i=1,2,…,n, let di be the degree of the vertex vi of G. The extended adjacency matrix Aex of G is defined so that its (i, j)-entry is equal to 12(didj+djdi) if the vertices vi and vj are adjacent, and 0 otherwise,Yang et al. (1994). The spectral radius η1 and the energy Eex of the Aex-matrix are examined. Lower and upper bounds on η1 and Eex are obtained, and the respective extremal graphs characterized.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:116-123
    DOI: 10.1016/j.amc.2016.10.029
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    References listed on IDEAS

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    1. Milovanović, Igor & Milovanović, Emina & Gutman, Ivan, 2016. "Upper bounds for some graph energies," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 435-443.
    2. Das, Kinkar Ch. & Mojallal, Seyed Ahmad & Gutman, Ivan, 2016. "On energy and Laplacian energy of bipartite graphs," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 759-766.
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    Cited by:

    1. 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.
    2. Bo Deng & Caibing Chang & Kinkar Chandra Das, 2023. "RETRACTED ARTICLE: The Sachs theorem and its application on extended adjacency matrix of graphs," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-12, January.
    3. Maryam Baghipur & Modjtaba Ghorbani & Shariefuddin Pirzada & Najaf Amraei, 2023. "On the Generalized Adjacency Spread of a Graph," Mathematics, MDPI, vol. 11(6), pages 1-9, March.
    4. Ghorbani, Modjtaba & Li, Xueliang & Zangi, Samaneh & Amraei, Najaf, 2021. "On the eigenvalue and energy of extended adjacency matrix," Applied Mathematics and Computation, Elsevier, vol. 397(C).

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