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

Shamaila Yousaf, Akhlaq Ahmad Bhatti and Akbar Ali

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

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.

Keywords: Chemical graph theory; Total irregularity index; Extremal trees; Segments; Branching vertices (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922001357
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001357

DOI: 10.1016/j.chaos.2022.111925

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().