TY - JOUR
ID - 13876
TI - A study on some properties of leap graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Naji, Ahmed M
AU - Davvaz, B.
AU - Mahde, Sultan S.
AU - Soner, N.D.
AD - Department of Mathematics, University of Mysore, Mysusu, India
AD - Department of Mathematics, Yazd University, Yazd, Iran
AD - Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore - 570 006, India
Y1 - 2020
PY - 2020
VL - 5
IS - 1
SP - 9
EP - 17
KW - Distance-degrees (of vertices)
KW - leap Zagreb indices
KW - leap graphs
DO - 10.22049/cco.2019.26430.1108
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13876.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13876_3e34a313e1c9a12cdfc1edc950e25098.pdf
ER -