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Pure Mathematics 2020
一类特殊三圈图的正负惯性指数和零度
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Abstract:
通过删除悬挂的树和压缩内部路等方法，给出了一类特殊三圈图的正负惯性指数和零度的计算方法。这类三圈图可分为I-和II-两个类型，我们得到以下结论：I-型三圈图的正负惯性指数(零度)等于一些树、单圈图和双圈图的正负惯性指数(零度)之和；II-型三圈图的正负惯性指数(零度)等于一些树和一些小的同类三圈图的正负惯性指数(零度)之和；对于那些小的三圈图的正负惯性指数和零度可以利用软件Matlab得到；还验证了对这类三圈图一个关于符号差的猜想成立。
By deleting pendant trees and compressing internal paths, a method of calculating the positive and negative inertia indexes and nullity of the one kind of tricyclic graphs is given. This kind of tricyclic graphs can be divided into I- and II-types. It is proved that the positive and negative inertia indexes and nullity of I-type tricyclic graphs are equal to the sum of some trees, unicyclic graphs and bicyclic graphs. The positive and negative inertia indexes and nullity of II-type tricyclic graphs are equal to the sum of some trees and small tricyclic graphs. The positive and negative inertia indexes and nullity of these small tricyclic graphs can be calculated by Matlab. And it is proved that a conjecture about sign difference is true for this kind of three-cycle graph.
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