%0 Journal Article
%T A study on some properties of leap graphs
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Naji, Ahmed M
%A Davvaz, B.
%A Mahde, Sultan S.
%A Soner, N.D.
%D 2020
%\ 06/01/2020
%V 5
%N 1
%P 9-17
%! A study on some properties of leap graphs
%K Distance-degrees (of vertices)
%K leap Zagreb indices
%K leap graphs
%R 10.22049/cco.2019.26430.1108
%X 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.
%U http://comb-opt.azaruniv.ac.ir/article_13876_3e34a313e1c9a12cdfc1edc950e25098.pdf