Study on Total Irregularity in Totally Segregated \(∞\) Bicyclic Graphs - Jorry, T. F. (Communications in Mathematics and Applications, 2021)
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 \(∞\) bicyclic graphs and identify the extremal graphs.