Pendant Graphs: Unveiling Regularity, Irregularity, and Support Vertices

This paper investigates Pendant Graphs, which are graphs that contain pendant vertices. It introduces a new perspective on the regularity and irregularity of pendant graphs, and discusses their relationship with Highly Irregular Graphs. Additionally, this work introduces a novel graph based on the concept derived from (m, k) Regular Graphs. The (m, k) regular graphs are closely related to Pendant Graph. The paper also delves into the nature and characteristics of pendant vertices. By exploring the characteristics of pendant vertices and defining the Cyclic Dendrimer Graph, the paper significantly contributes to both Graph Theory and Chemical Graph Theory.