Author/Authors :
Naji, Ahmed M Department of Studies in Mathematics - University of Mysore, Manasagangotri Mysore - 570 006, India , Davvaz, B Department of Mathematics - Yazd University, Yazd, Iran , Mahde, Sultan S Department of Studies in Mathematics - University of Mysore, Manasagangotri Mysore - 570 006, India , Soner, N.D Department of Studies in Mathematics - University of Mysore, Manasagangotri Mysore - 570 006, India
Abstract :
In a graph G, the rst and second degrees of a vertex v are equal to the
number of their rst and second neighbors and are denoted by d(v=G) and d2(v=G),
respectively. The rst, second and third leap Zagreb indices are the sum of squares
of second degrees of vertices of G, the sum of products of second degrees of pairs of
adjacent vertices in G and the sum of products of rst and second degrees of vertices of
G, respectively. In this paper, we initiate in studying a new class of graphs depending
on the relationship between rst and second degrees of vertices and is so-called a leap
graph. Some properties of the leap graphs are presented. All leap trees and fC3;C4g-
free leap graphs are characterized.
