图的Nirmala指数的极值

Extremal Values of Nirmala Index of Graphs

自图的第一个拓扑指数被定义以来,研究者们给出了许多种拓扑指数的定义,这些拓扑指数被广泛地应用于化学、生物、网络科学等相关学科。近年来,研究者们给出了图的Nirmala指数的定义,得到了Nir-mala指数的数学性质以及Nirmala指数与其他拓扑指数之间的关系。通过定义图的运算来研究Nirmala指数的极值,利用辅助函数确定了树的第二大Nirmala指数,在得到了若干图类的Nirmala指数的界的同时,完全刻画了具有这些界的极图,并利用Karamata不等式确定了单圈图类中Nirmala指数的极值。

Since the first topological index of graph was defined,many kinds of topological index definitions have been given by researchers,which are widely used in chemistry,biology,network science and other related disci-plines.Recently,the definition of Nirmala index of graphs was given,the mathematical properties of the Nirmala in-dex and the relationship between the Nirmala index and other topological indices have been obtained.The extreme value of Nirmala index is studied by the operation of defining graph,and the second largest Nirmala index of the tree is determined by auxiliary function.The Nirmala index bounds of several graph classes are obtained,and the po-lar graphs with these bounds are described completely.The extreme value of Nirmala exponent in the class of unicy-clic graphs is determined by Karamata inequality.