Effect of Vertex and Edge Deletion on Total Irregularity Index

Cut vertices and bridges are significant graph parts that help to separate large graphs into smaller ones to ease the calculations that need to be made by means of smaller and easier steps. Recently, the effect of removing such graph parts on several topological graph indices has been calculated. Removal of a vertex means that a member is discarded from a network together with the member's connections, and removal of an edge corresponds to removing the connection between two members in the network. Thus, the reliability of a network can be increased by removing some unwanted vertices and edges from the network by using the formulas provided here for several vertex and edge types. This paper considers the effect of vertex and edge removal on the total irregularity index. It removes several different vertex and edge types from a network and calculates their effects on the total irregularity index. The method employed here can be applied to other irregularity indices and even to other graph-theoretical indices to measure the effect of vertex or edge removal on such indices.