论文标题
关于具有给定度序列的连接图的Sombor索引的注释
Note on Sombor index of connected graphs with given degree sequence
论文作者
论文摘要
对于简单的连接图$ g =（v，e）$，让$ d（u）$是$ g $的顶点$ u $的程度。 $ g $的通用Sombor索引定义为$$so_α（g）= \ sum_ {uv \ in E} \ left [d（u）^2+d（v）^2 \ right]^α$$，其中$ so（g）= so so_ {0.5}（g）$是最近发明的Sombor Index。在本文中，我们表明，在具有固定度序列的连接图中（最低度等于一个），存在一种特殊的极值$ bfs $ - $ -Graph，最低限度的Sombor索引（$ 0 <α<1 $）（分别为$α> 1 $或$ $α<0 <0 <0 $ $ 0 <α<1 $）。此外，对于任何给定的树，单周期和双环度序列，具有最低度1的序列，存在一个独特的极值$ bfs $ - 带有最低通用Sombor索引的$ 0 <α<1 $ $ 0 <α<1 $，最大SOMBOR索引，对于$α> 1 $或$ $α<0 $。
For a simple connected graph $G=(V,E)$, let $d(u)$ be the degree of the vertex $u$ of $G$. The general Sombor index of $G$ is defined as $$SO_α(G)=\sum_{uv\in E} \left[d(u)^2+d(v)^2\right]^α$$ where $SO(G)=SO_{0.5}(G)$ is the recently invented Sombor index. In this paper, we show that in the class of connected graphs with a fixed degree sequence (for which the minimum degree being equal to one), there exists a special extremal $BFS$-graph with minimum general Sombor index for $0<α<1$ (resp. maximum general Sombor index for either $α>1$ or $α<0$). Moreover, for any given tree, unicyclic, and bicyclic degree sequences with minimum degree 1, there exists a unique extremal $BFS$-graph with minimum general Sombor index for $0<α<1$ and maximum general Sombor index for either $α>1$ or $α<0$.
