A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index

Abstract

In 2010, Vukičević introduced an new graph invariant, the inverse sum indeg index of a graph, which has been studied due to its wide range of applications. Let Bnd be the class of bipartite graphs of order n and diameter d. In this paper, we mainly characterize the bipartite graphs in Bnd with the maximal inverse sum indeg index. Bipartite graphs with the largest, second-largest, and smallest inverse sum indeg indexes are also completely characterized.

Keywords

• the inverse sum indeg index
• bipartite graphs
• diameter
• extremal graphs