论文标题
树木的最小原子键 - 汇总指数，其固定顺序和/或吊坠的数量
Minimum Atom-Bond Sum-Connectivity Index of Trees With a Fixed Order and/or Number of Pendent Vertices
论文作者
论文摘要
令$ d_u $为图$ g $的顶点$ u $的程度。图$ g $的原子键汇总 - 连接性（ABS）索引是数字$（1-2（d_v+d_w）^{ - 1}）^{1/2} $的总和。本文给出了具有固定数量的吊坠顶点的所有树类中具有最小ABS指数的图表的表征；恒星是上述图类别中独特的极端图。还解决了确定具有$ n $顶点和$ p $ dentent顶点的所有树类中具有最低ABS指数的图形的问题；当$ n \ ge 3p-2 \ ge7 $时，这种极端树具有最高学位$ 3 $，而平衡的双星是案例$ p = n-2 $的唯一极端树。
Let $d_u$ be the degree of a vertex $u$ of a graph $G$. The atom-bond sum-connectivity (ABS) index of a graph $G$ is the sum of the numbers $(1-2(d_v+d_w)^{-1})^{1/2}$ over all edges $vw$ of $G$. This paper gives the characterization of the graph possessing the minimum ABS index in the class of all trees of a fixed number of pendent vertices; the star is the unique extremal graph in the mentioned class of graphs. The problem of determining graphs possessing the minimum ABS index in the class of all trees with $n$ vertices and $p$ pendent vertices is also addressed; such extremal trees have the maximum degree $3$ when $n\ge 3p-2\ge7$, and the balanced double star is the unique such extremal tree for the case $p=n-2$.
