Some Properties and Topological Indices of k-nested Graphs

A double nested graph is a bipartite graph with the property that the neighborhood of vertices of each partite set form a chain with respect to set inclusion. Motivated by this structure, we generalize and define a new class of graphs and name it as k-nested graphs and study its properties. Characterization of a k-nested 2-self centered graph which is edge maximal is discussed and also we show that none of the k-nested 2-self centered graph is edge minimal. We extend the study and gave the bounds for Wiener index and some Szeged indices of k-nested graphs.We conclude this article by exploring some more degree based topological indices of k-nested graphs.