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Note on non-regular graphs with minimal total irregularity

Author

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  • Ashrafi, Ali Reza
  • Ghalavand, Ali

Abstract

Let G be a graph with vertex set V(G). The total irregularity of G is defined as irrt(G)=∑{u,v}⊆V(G)|degG(u)−degG(v)|, where degG(v) is the degree of the vertex v of G. The aim of this paper is to present some bounds for this graph invariant. A new simple proof for a recently proposed conjecture on total irregularity of graphs is also presented.

Suggested Citation

  • Ashrafi, Ali Reza & Ghalavand, Ali, 2020. "Note on non-regular graphs with minimal total irregularity," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308835
    DOI: 10.1016/j.amc.2019.124891
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    References listed on IDEAS

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    1. Lihua You & Jieshan Yang & Yingxue Zhu & Zhifu You, 2014. "The Maximal Total Irregularity of Bicyclic Graphs," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, April.
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