Abstract
Many measures of irregularity were introduced and studied before. Among them, the most investigated one is the Total Irregularity of a graph defined by Abdo et al. (The total irregularity of a graph, Discrete Mathematics and Theoretical Computer Science 16(1) (2014), 201 – 206). It is defined as sum of absolute values of difference of vertex degrees over all vertices of the graph. A graph in which every two adjacent vertices have distinct degrees is totally segregated. Here, we find the greatest Total Irregularity of Totally Segregated \(\infty\) bicyclic graphs and identify the extremal graphs.
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