CAJ | 학술논문

图论中的一个核心问题是研究图的不变量。对于给定的一个平图，可以建立该图的T utte多项式不变量。一直以来，认为 T utte 多项式是最一般的图的不变量。经典的T utte多项式不变量是含有2个变元 x ，y的多项式，但是这个多项式却不能区分所有的图。这促使我们考虑可以通过增加变元的方法来细分图的类别。对于给定一个的平图，将图的T utte多项式不变量进行了推广，得到一个新的 n变元多项式，并证明其是图的不变量。进而，也验证它能区分T utte多项式不能区分的一类图，这类图是给定的一个图与在这个图上再加一些与之不相交的点。
도론중적일개핵심문제시연구도적불변량。대우급정적일개평도，가이건립해도적T utte다항식불변량。일직이래，인위 T utte 다항식시최일반적도적불변량。경전적T utte다항식불변량시함유2개변원 x ，y적다항식，단시저개다항식각불능구분소유적도。저촉사아문고필가이통과증가변원적방법래세분도적유별。대우급정일개적평도，장도적T utte다항식불변량진행료추엄，득도일개신적 n변원다항식，병증명기시도적불변량。진이，야험증타능구분T utte다항식불능구분적일류도，저류도시급정적일개도여재저개도상재가일사여지불상교적점。
An important problem is the invariant of graph in graph theory .Given a planar graph ,we can build the Tutte polynomial invariant .For a long time ,we think Tutte polynomial is the most general graph invariant .Classic Tutte polynomial invariant contained two variable ,but this polyno‐mial was not able to distinguish among all of the graphs .Thus we consider to move through the way to increase the variable to the category of the subdivision graph .In this paper ,given a graph ,we will generalize Tutte polynomial invariant ,get a new variable polynomial ,and prove its invariance .Fur‐thermore ,we also verify that it can distinguish a class diagram which is given a graph and added some intersection points in this graph .The class diagram can’t be distinguished between the classic Tutte polynomials .