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

作　　者：王星雨 耿显亚 Wang Xingyu;Geng Xianya(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《洛阳师范学院学报》2024年第2期7-9,共3页Journal of Luoyang Normal University

基　　金：国家自然科学基金项目(12171190);安徽省自然科学基金项目(2008085MAO1)。

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SO kα(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Sombor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.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 SO kα(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 eitherα>1 orα<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 eitherα>1 orα<0.

关 键 词：k阶Sombor指数 度序列 优化 BFS图 

分 类 号：O157.5[理学—数学]