论文标题
第二个Zagreb索引的指数相对于最大树
The maximal tree with respect to the exponential of the second Zagreb index
论文作者
论文摘要
第二个Zagreb索引是$ m_2（g）= \ sum_ {uv \ in E（g）} d_ {g}（u）d_ {g}（g}（v）$。发现它发生在交替碳氢化合物的总$π$ - 电子能量的某些近似表达中，并在其QSPR和QSAR研究中使用。最近引入了基于顶点的拓扑指数的指数。众所周知，在所有具有$ n $顶点的树中，第二个Zagreb索引$ e^{m_2} $的指数在路径$ p_n $中达到其最小值。在本文中，我们表明$ e^{m_2} $用$ n $ vertices在平衡的双星中达到其最大值，并解决了克鲁兹和拉达提出的一个开放问题[R. Cruz，J。Rada，《路径和恒星》是树木中基于顶点学位的拓扑指数的极端价值，Match Commun。数学。计算。化学82（3）（2019）715-732]。
The second Zagreb index is $M_2(G)=\sum_{uv\in E(G)}d_{G}(u)d_{G}(v)$. It was found to occur in certain approximate expressions of the total $π$-electron energy of alternant hydrocarbons and used by various researchers in their QSPR and QSAR studies. Recently the exponential of a vertex-degree-based topological index was introduced. It is known that among all trees with $n$ vertices, the exponential of the second Zagreb index $e^{M_2}$ attains its minimum value in the path $P_n$. In this paper, we show that $e^{M_2}$ attains its maximum value in the balanced double star with $n$ vertices and solve an open problem proposed by Cruz and Rada [R. Cruz, J. Rada, The path and the star as extremal values of vertex-degree-based topological indices among trees, MATCH Commun. Math. Comput. Chem. 82 (3) (2019) 715-732].
