TY - JOUR
ID - 13782
TI - Leap Zagreb indices of trees and unicyclic graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Gutman, Ivan
AU - Shao, Zehui
AU - Li, Zepeng
AU - Wang, ShaohuiShaohui
AU - We, Pu
AD - University of Kragujevac
AD - Guangzhou University
AD - Lanzhou University
AD - Department of Mathematics and Computer Science, Adelphi University,
Garden City, NY, USA.
AD - Guangzhou University,
Y1 - 2018
PY - 2018
VL - 3
IS - 2
SP - 179
EP - 194
KW - Leap Zagreb index
KW - Zagreb index
KW - degree (of vertex)
DO - 10.22049/cco.2018.26285.1092
N2 - By $d(v|G)$ and $d_2(v|G)$ are denoted the number of first and second neighbors of the vertex $v$ of the graph $G$. The first, second, and third leap Zagreb indices of $G$ are defined as $LM_1(G) = sum_{v in V(G)} d_2(v|G)^2$, $LM_2(G) = sum_{uv in E(G)} d_2(u|G),d_2(v|G)$, and $LM_3(G) = sum_{v in V(G)} d(v|G),d_2(v|G)$, respectively. In this paper, we generalize the results of Naji et al. [Commun. Combin. Optim. {bf 2} (2017), 99--117], pertaining to trees and unicyclic graphs. In addition, we determine upper and lower bounds on these leap Zagreb indices and characterize the extremal graphs.
UR - http://comb-opt.azaruniv.ac.ir/article_13782.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13782_6ae3457e7f09b8f6c913dd0fa53fa742.pdf
ER -