What question did this study set out to answer?

The aim is to identify tetracyclic graphs that achieve the smallest total irregularity index.

February 12, 2026Open Access

On the minimum total irregularity index of tetracyclic graphs

HAH. AhmedNational University of Computer and Emerging Sciences ABAkhlaq Ahmad BhattiNational University of Computer and Emerging Sciences SYShamaila YousufUniversity of Gujrat

Key Points

The aim is to identify tetracyclic graphs that achieve the smallest total irregularity index.
Defined total irregularity index based on vertex degree differences.
Analyzed fixed-order tetracyclic graphs with n vertices and n + 3 edges.
Calculated total irregularity for various tetracyclic graph configurations.
Identified graphs that minimally achieve the total irregularity index.
Calculated the first two smallest total irregularity values among the graphs considered.

Abstract

The total irregularity of a graph G is defined as the sum of the absolute values of the differences of vertex degrees over all unordered pairs of vertices of G. In the present paper, the problem of determining graphs attaining the first two smallest values of the total irregularity index among all fixed-order tetracyclic graphs is addressed, where an n-order tetracyclic graph is a connected graph with n vertices and n + 3 edges.

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