Extremal first leap Zagreb index of k-generalized quasi-trees
Received:March 26, 2021  Revised:October 12, 2021
Key Word: k-generalized quasi-trees   the first leap Zagreb indices   2-distance degree.  
Fund ProjectL:the Foundation of Henan Department of Science and Technology (182102310830), the Foundation of Henan University of Engineering (D2016018), the Foundation of Henan Educational Committee (20A110016) and the Foundation of Henan Educational Committee (2020GGJS239)
Author NameAffiliationAddress
Pei Sun Zhengzhou University of Aeronautics No.115, wenyuanxi Road, zhengdong xin estates,zhengzhou city, Henan province, P.R.China
Kai Liu Henan University of Engineering No. 1, Xianghe Road, Xinzheng, P. R. China
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      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.
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