两图运算后Sombor指数的上界

The Upper Bound of Sombor Index After Two Graph Operations

Sombor指数是基于顶点度引入的一种新的化学拓扑指数。本文研究了两个有限简单的连通图经过连接运算、笛卡尔积运算、冠运算、字典序积运算、对称差运算后的Sombor指数,并且刻画了其极图。首先,对每种运算后表达式的边进行了分类。然后,利用顶点的最大度并结合不等式放缩,给出了各运算图Sombor指数上界的估值不等式。最后,证明了取得Sombor指数上界的条件为两图都是正则图。

Sombor index is a new chemical topological index introduced based on vertex degree.The Sombor index of two finite simple connected graphs is studied after five graph operations(i.e.,connec‐tion operation,Cartesian product operation,crown operation,dictionary order product operation,and sym‐metric difference operation),and their extremal graphs are described.Firstly,the edges of the expres‐sions after each operation are classified.Then a valuation inequality for the upper bound of the Sombor index of the graphs of each operation is given by using the maximum degree of the vertices and the inequal‐ity deflation.Finally,the condition of obtaining the upper bound of Sombor index is given to be that both graphs are regular graphs.