$k$-广义拟树的第一个leap Zagreb 指标

Extremal First Leap Zagreb Index of $k$-Generalized Quasi-Trees

中文关键词:  $k$-广义拟树  第一个leap Zagreb 指标  2-距离点

英文关键词:$k$-generalized quasi-trees  the first leap Zagreb index  $2$-distance degree

中文摘要:

      图$G$的第一个leap Zagreb指标定义如下: $LM_1(G)=\sum_(v\in v(G)}d_2(v/G)^2$, 其中$d_2(v/G)$是离点$v$的距离为2的顶点. 令$\mathcal{QT}^{(k)}(n)$是有$n$个顶点的$k$-广义拟树的集合.若$G\in \mathcal{QT}^{(k)}(n)$, 本文给出了图$G$的第一个leap Zagreb指标的范围.

英文摘要:

      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.