On the Extremal Narumi-Katayama Index of Graphs

The Narumi-Katayama index of a graph G, denoted by NK(G), is defined as Πni=1 deg(vi). In this paper, we determine the extremal NK(G) of trees, unicyclic graphs with given diameter and vertices. Moreover, the second and third minimal NK(G) of unicyclic graphs with given vertices and the minimal NK(G) of bicyclic graphs with given vertices are obtained.