This work determines the smallest total irregularity index values in tetracyclic graphs, suggesting optimal graph structures.
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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Ahmed et al. (2025) studied this question.
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