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On energy and Laplacian energy of bipartite graphs

Author

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  • Das, Kinkar Ch.
  • Mojallal, Seyed Ahmad
  • Gutman, Ivan

Abstract

Let G be a bipartite graph of order n with m edges. The energy E(G) of G is the sum of the absolute values of the eigenvalues of the adjacency matrix A. In 1974, one of the present authors established lower and upper bounds for E(G) in terms of n, m, and detA. Now, more than 40 years later, we correct some details of this result and determine the extremal graphs. In addition, an upper bound on the Laplacian energy of bipartite graphs in terms of n, m, and the first Zagreb index is obtained, and the extremal graphs characterized.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:759-766
    DOI: 10.1016/j.amc.2015.10.047
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    References listed on IDEAS

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    1. Renqian, Suonan & Ge, Yunpeng & Huo, Bofeng & Ji, Shengjin & Diao, Qiangqiang, 2015. "On the tree with diameter 4 and maximal energy," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 364-374.
    2. Das, Kinkar Ch. & Mojallal, Seyed Ahmad & Gutman, Ivan, 2015. "On Laplacian energy in terms of graph invariants," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 83-92.
    3. Li, Xueliang & Qin, Zhongmei & Wei, Meiqin & Gutman, Ivan & Dehmer, Matthias, 2015. "Novel inequalities for generalized graph entropies – Graph energies and topological indices," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 470-479.
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    Citations

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    Cited by:

    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.
    2. Rodríguez, José M. & Sigarreta, José M., 2016. "Spectral properties of geometric–arithmetic index," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 142-153.
    3. Yan, Xiaohe & Gu, Chenghong & Li, Furong & Xiang, Yue, 2018. "Network pricing for customer-operated energy storage in distribution networks," Applied Energy, Elsevier, vol. 212(C), pages 283-292.

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