论文标题
$ k $ -apex树，具有最小增强的Zagreb索引
The $k$-apex trees with minimum augmented Zagreb index
论文作者
论文摘要
对于至少三个顶点上的连接图$ g $，增强的Zagreb索引（azi）为$ g $，定义为$$ azi（g）= \ sum_ {uv \ in E（g）} \ left（\ frac {\ frac {d（d（u）d（u）d（u）d（v）d（d（u）d（u）索引与亨氏和辛坦斯的形成热相关。 $ k $ -apex树$ g $是一个连接的图，承认$ k $ -subset $ x \ subset v（g）$，因此$ g-x $是一棵树，而$ g-s $不是任何$ s \ subset v（g）$ subset v（g）$ hastinatity的$ k $。通过调查$ k $ -apex树的某些结构性属性，我们可以识别出所有$ n $ dertices上所有$ k $ -apex树中Azi的图形，$ k \ ge 4 $和$ n \ ge 3（k+1）$。后者解决了[K. Cheng，M。Liu，F。Belardo，{\ em Appl。数学。 comput。}，{\ bf402}（2021），126139]。
For a connected graph $G$ on at least three vertices, the augmented Zagreb index (AZI) of $G$ is defined as $$AZI(G)=\sum_{uv\in E(G)}\left(\frac{d(u)d(v)}{d(u)+d(v)-2}\right)^{3},$$ being a topological index well-correlated with the formation heat of heptanes and octanes. A $k$-apex tree $G$ is a connected graph admitting a $k$-subset $X\subset V(G)$ such that $G-X$ is a tree, while $G-S$ is not a tree for any $S\subset V(G)$ of cardinality less than $k$. By investigating some structural properties of $k$-apex trees, we identify the graphs minimizing the AZI among all $k$-apex trees on $n$ vertices for $k\ge 4$ and $n\ge 3(k+1)$. The latter solves an open problem posed in [K. Cheng, M. Liu, F. Belardo, {\em Appl. Math. Comput.}, {\bf402} (2021), 126139].
