# On the extremal total irregularity index of n-vertex trees with fixed maximum degree

Document Type : Original paper

Authors

Fast NUCES, Lahore, Pakistan.

Abstract

In the extension of irregularity indices, Abdo et. al. {[H. Abdo, S. Brandt, D. Dimitrov, The total irregularity of a graph, Discrete Math. Theor. Comput. Sci. 16  (2014), 201--206]} defined the total irregularity of a graph $G = (V,E)$ as $irr_{t}(G)= \frac{1}{2} \sum_{u,v\in V(G)} \big|d_u - d_v \big|$, where $d_u$ denotes the vertex degree of a vertex $u \in V(G)$. In this paper, we investigate the total irregularity of trees with bounded maximal degree $\Delta$ and state integer linear programming problem which gives standard information about extremal trees and it also calculates the index.

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Main Subjects

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