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On total irregularity index of trees with given number of segments or branching vertices

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  • Yousaf, Shamaila
  • Bhatti, Akhlaq Ahmad
  • Ali, Akbar

Abstract

A non-negative graph invariant IM is said to be an irregularity measure of a graph G if the following condition holds: IM(G)=0 if and only if G is regular. There exist many irregularity measures in the literature and the Albertson index is probably the most studied such measure. In order to overcome several drawbacks of the Albertson index, a variant of the Albertson index was recently introduced under the name ǣtotal irregularityǥ. The total irregularity index of a graph G is defined as 12∑u,w∈V(G)|degG(u)−degG(w)|, where degG(w) is the degree of a vertex w∈V(G). By an n-vertex tree, we mean a tree of order n. In the present study, the best possible sharp upper and lower bounds on the total irregularity index of n-vertex trees with fixed number of segments or branching vertices are derived.

Suggested Citation

  • Yousaf, Shamaila & Bhatti, Akhlaq Ahmad & Ali, Akbar, 2022. "On total irregularity index of trees with given number of segments or branching vertices," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001357
    DOI: 10.1016/j.chaos.2022.111925
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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.
    2. Slim Belhaiza & Nair Maria Maia Abreu & Pierre Hansen & Carla Silva Oliveira, 2005. "Variable Neighborhood Search for Extremal Graphs. XI. Bounds on Algebraic Connectivity," Springer Books, in: David Avis & Alain Hertz & Odile Marcotte (ed.), Graph Theory and Combinatorial Optimization, chapter 0, pages 1-16, Springer.
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    Cited by:

    1. Raza, Zahid & Akhter, Shehnaz, 2023. "On maximum Zagreb connection indices for trees with fixed domination number," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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