A study on some properties of leap graphs

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 d2(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 {C3, C4}- free leap graphs are characterized.

Keywords

• distance-degrees (of vertices)
• leap zagreb indices
• leap graphs