论文标题
第二索姆博尔指数的极端值的分子树
Molecular trees with extremal values of the second Sombor index
论文作者
论文摘要
Gutman引入了图形不变的新几何背景，最简单的是第二个Sombor索引$ so_2 $，定义为$ so_2 = so_2 = so_2（g）= \ sum_ {uv \ in e} \ in e} \ frac {| d^2_g（| d^2_g（u）-d^2_g（u）-d^2_g（U）-d^2_g（v） $ g =（v，e）$是一个简单的图，$ d_g（v）$表示$ g $中的$ v $的度。在本文中，研究了第二Sombor指数的化学适用性，并且显示第二SOMBOR指数可用于预测具有很高准确性的物理化学性质，与一些公认且经常使用的指数相比。同样，我们在所有（分子）树中获得了第二个SOMBOR指数的结合，这些树木具有固定数量的顶点，并表征了那些实现极值的分子树。
A new geometric background of graph invariants was introduced by Gutman, of which the simplest is the second Sombor index $SO_2$, defined as $SO_2=SO_2(G)=\sum_{uv\in E}\frac{|d^2_G(u)-d^2_G(v)|}{d^2_G(u)+d^2_G(v)}$, where $G = (V, E)$ is a simple graph and $d_G(v)$ denotes the degree of $v$ in $G$. In this paper, the chemical applicability of the second Sombor index is investigated and it is shown that the the second Sombor index is useful in predicting physicochemical properties with high accuracy compared to some well-established and often used indices. Also, we obtain a bound for the second Sombor index among all (molecular) trees with fixed numbers of vertices, and characterize those molecular trees achieving the extremal value.
