%0 Journal Article %T On the extremal total irregularity index of n-vertex trees with fixed maximum degree %J Communications in Combinatorics and Optimization %I Azarbaijan Shahid Madani University %Z 2538-2128 %A Adeel, Shamaila %A Bhatti, Akhlaq Ahmad %D 2021 %\ 06/01/2021 %V 6 %N 1 %P 113-121 %! On the extremal total irregularity index of n-vertex trees with fixed maximum degree %K Irregularity %K total irregularity index %K maximal degree %K molecular trees %K integer linear programming problem %R 10.22049/cco.2020.26965.1168 %X 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. %U http://comb-opt.azaruniv.ac.ir/article_14102_142e6efb502f59a1a401d057893b27df.pdf