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; C4gfree leap graphs are characterized.