给定度序列的连通图类的k阶Sombor指数
The k-order Sombor Index Connected Graphs with Given Degree Sequence
王星雨 1耿显亚1
作者信息
- 1. 安徽理工大学 数学与大数据学院,安徽 淮南 232001
- 折叠
摘要
对于一个简单连通图G =(V,E),d(u)是图G的顶点u的度.G的k阶Sombor指数被定义为SOkα(G)= ∑ uv∈E[d(u)k + d(v)k]α,k ∈{2,3,…,n}.给出了在给定度序列的连通图类(最小度为1)中,存在一个特殊极BFS图,当0<α<1 时,具有最小k阶Som-bor指数;当α>1 或α<0 时,具有最大k阶Sombor指数.并且,任意给定度序列(最小度为1)的树,单圈图和双圈图中,当0<α<1 时,存在唯一极图具有最小k阶Sombor指数;当α>1 或α<0 时,具有最大k阶Sombor指数.
Abstract
For the simple connected graph G =(V,E),d(u)is the degree of the vertex u of G.The k-order Sombor index of G is defined as SOkα(G)=∑ uv∈E[d(u)k + d(v)k]α,k ∈{2,3,…,n}.The result shows 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 and maximum general Sombor index for either α>1or 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>1or α<0.
关键词
k阶Sombor指数/度序列/优化/BFS图Key words
k-order Sombor index/degree sequence/optimization/BFS-graph引用本文复制引用
基金项目
国家自然科学基金(12171190)
安徽省自然科学基金(2008085MAO1)
出版年
2024
NETL
NSTL
万方数据