四类运算图的Sombor指数

Sombor index on four operation graphs

设图G是一个简单图,E(G)为G的边集,du,dv分别为顶点u,v的度.本文在图的S(G)、R(G)、Q(G)、T(G)4种变换运算和两图的笛卡尔积相结合的F-和定义基础上,利用最大度,通过分类讨论的方法,计算了四种相关运算图的Sombor指数的上界,并且刻画了相应的极值。

Let G be a simple graph,E(G)be the edge set of G,and,du,dv be the degree of vertex u,v,respectively.In this paper,we focuse on the definition of F-sum of graphs combined with four transformation operations S(G),R(G),Q(G),T(G)and Cartesian product of two graphs,and calculate the upper bound of the Sombor index of the four kinds of related graphs by using the maximum degree and classification,and characterize their extreme values.