| Extremal First Leap Zagreb Index of $k$-Generalized Quasi-Trees |
| Received:March 26, 2021 Revised:September 22, 2021 |
| Key Words:
$k$-generalized quasi-trees the first leap Zagreb index $2$-distance degree
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| Fund Project:Supported by the Foundation of Henan Department of Science and Technology (Grant No.182102310830), the Foundation of Henan University of Engineering (Grant No.D2016018) and the Foundation of Henan Educational Committee (Grant Nos.20A110016; 2020GGJS239). |
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| Abstract: |
| For a graph $G$, the first leap Zagreb index is defined as $LM_1(G)=\sum_{v\in V(G)}d_2(v/G)^2$, where $d_2(v/G)$ is the $2$-distance degree of a vertex $v$ in $G$. Let $\mathcal{QT}^{(k)}(n)$ be the set of $k$-generalized quasi-trees with $n$ vertices. In this paper, we determine the extremal elements from the set $\mathcal{QT}^{(k)}(n)$ with respect to the first leap Zagreb index. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.03.001 |
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