@article {
author = {Naji, Ahmed and Davvaz, B. and Mahde, Sultan S. and Soner, N.D.},
title = {A study on some properties of leap graphs},
journal = {Communications in Combinatorics and Optimization},
volume = {5},
number = {1},
pages = {9-17},
year = {2020},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26430.1108},
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.},
keywords = {Distance-degrees (of vertices),leap Zagreb indices,leap graphs},
url = {http://comb-opt.azaruniv.ac.ir/article_13876.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13876_3e34a313e1c9a12cdfc1edc950e25098.pdf}
}