On leap Zagreb indices of graphs

Abstract

The first and second Zagreb indices of a graph are equal‎, ‎respectively‎, ‎to‎ ‎the sum of squares of the vertex degrees‎, ‎and the sum of the products of‎ ‎the degrees of pairs of adjacent vertices‎. ‎We now consider analogous‎ ‎graph invariants‎, ‎based on the second degrees of vertices (number of‎ ‎their second neighbors)‎, ‎called leap Zagreb indices‎. ‎A number of their‎ ‎basic properties is established‎.

Keywords

• Degree (of vertex)‎
• ‎Second degree‎
• ‎Zagreb‎ ‎indices‎
• ‎Leap Zagreb indices