Computation of Leap Zagreb Indices of Some Windmill Graphs

Abstract

Recently, A. M. Naji [13], introduced leap Zagreb indices of a graph based on the second degrees of vertices (number of their second neighbours). The first leap Zagreb index $L M_1(G)$ is equal to the sum of squares of the second degrees of the vertices, the second leap Zagreb index $L M_2(G)$ is equal to the sum of the products of the second degrees of pairs of adjacent vertices of G and the third leap Zagreb index $L M_3(G)$ is equal to the sum of the products of the first degrees with the second degrees of the vertices. In this paper, we computing Leap Zagreb indices of windmill graphs such as French windmill graph $F^m_n$, Dutch windmill graph $D^m_n$, Kulli cycle windmill graph $C^m_{n+1}$, and Kulli path windmill graph $P^m_{n+1}$.