# A study on some properties of leap graphs

Document Type : Original paper

Authors

1 Department of Mathematics, University of Mysore, Mysusu, India

2 Department of Mathematics, Yazd University, Yazd, Iran

3 Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India

Abstract

In a graph $G$, the first and second degrees of a vertex $v$ are equal to the number of their first and second neighbors and are denoted by $d(v/G)$ and $d_2(v/G)$, respectively. The first, 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 first 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 first and second degrees of vertices and is so-called a leap graph. Some properties of the leap graphs are presented. All leap trees and $\{C_3, C_4\}$-free leap graphs are characterized.

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