Leap Zagreb Indices of Trees and Unicyclic Graphs
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 $LM_1(G) = \sum_{v \in V(G)} d_2(v|G)^2$, $LM_2(G) = \sum_{uv \in E(G)} d_2(u|G)\,d_2(v|G)$, ...
Main Authors: | , , , , |
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Format: | Article |
Language: | English |
Published: |
Azarbaijan Shahide Madani University
2018-06-01
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Series: | Communications in Combinatorics and Optimization |
Subjects: | |
Online Access: | http://comb-opt.azaruniv.ac.ir/article_13782.html |
Summary: | 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. |
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ISSN: | 2538-2128 2538-2136 |