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 is 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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Main Subjects