THE HYPER-ZAGREB INDEX OF SOME DERIVED GRAPHS

Abstract

Let  be a connected graph.  The hyper-Zagreb index is defined as    In this paper, comparison of the hyper-Zagreb index and other degree based topological indices like the Forgotten index, Zagreb and Banhatti indices of some derived graphs such as line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph and total graph are obtained.  In addition, exact values of some standard graphs of above derived graphs are presented.