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Some new spectral bounds for graph irregularity

Author

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  • Chen, Xiaodan
  • Hou, Yaoping
  • Lin, Fenggen

Abstract

The irregularity of a simple graph G=(V,E) is defined as irr(G)=∑uv∈E(G)|dG(u)−dG(v)|,where dG(u) denotes the degree of a vertex u ∈ V(G). This graph invariant, introduced by Albertson in 1997, is a measure of the defect of regularity of a graph. Recently, it also gains interest in Chemical Graph Theory, where it is named the third Zagreb index. In this paper, by means of the Laplacian eigenvalues and the normalized Laplacian eigenvalues of G, we establish some new spectral upper bounds for irr(G). We then compare these new bounds with a known bound by Goldberg, and it turns out that our bounds are better than the Goldberg bound in most cases. We also present two spectral lower bounds on irr(G).

Suggested Citation

  • Chen, Xiaodan & Hou, Yaoping & Lin, Fenggen, 2018. "Some new spectral bounds for graph irregularity," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 331-340.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:331-340
    DOI: 10.1016/j.amc.2017.09.038
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    Citations

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    Cited by:

    1. Gutman, Ivan, 2018. "Stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 234-238.
    2. Gu, Tianqi & Kim, Inhi & Currie, Graham, 2019. "To be or not to be dockless: Empirical analysis of dockless bikeshare development in China," Transportation Research Part A: Policy and Practice, Elsevier, vol. 119(C), pages 122-147.
    3. Abdo, Hosam & Dimitrov, Darko & Gutman, Ivan, 2019. "Graph irregularity and its measures," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 317-324.
    4. Sandra Bestakova, 2019. "The Influence Of Short-Term Rental On Rental Housing Prices In Prague," Proceedings of Business and Management Conferences 8512235, International Institute of Social and Economic Sciences.
    5. Wei Gao & Muhammad Aamir & Zahid Iqbal & Muhammad Ishaq & Adnan Aslam, 2019. "On Irregularity Measures of Some Dendrimers Structures," Mathematics, MDPI, vol. 7(3), pages 1-15, March.
    6. Sakander Hayat & Amina Arif & Laiq Zada & Asad Khan & Yubin Zhong, 2022. "Mathematical Properties of a Novel Graph-Theoretic Irregularity Index with Potential Applicability in QSPR Modeling," Mathematics, MDPI, vol. 10(22), pages 1-24, November.

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