一类特殊三圈图的正负惯性指数和零度
Positive and Negative Inertia Indexes and Nullity of One Special Kinds of Tricyclic Graphs
DOI: 10.12677/PM.2020.107075, PDF,    国家自然科学基金支持
作者: 解承玲*, 马海成：青海民族大学，数学与统计学院，青海 西宁
关键词: 三圈图；正惯性指数；负惯性指数；零度；Tricyclic Graphs； Positive Inertia Index； Negative Inertia Index； Nullity
摘要: 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。
Abstract: 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.
文章引用：解承玲, 马海成. 一类特殊三圈图的正负惯性指数和零度[J]. 理论数学, 2020, 10(7): 623-630. https://doi.org/10.12677/PM.2020.107075

参考文献

[1] Cvetković, D., Doob, M. and Sachs, H. (1980) Spectra of Graphs-Theory and its Application. Academic Press, New York.
[2] Ma, H.C., Yang, W.H. and Li, S.G. (2013) Positive and Negative Inertia Index of a Graph. Linear Algebra and its Applications, 438, 331-341. [Google Scholar] [CrossRef] 
[3] Collatz, V.L. and Sinogowitz, U. ()1957 Spektren Endlicher Grafen. Abhandlungen aus dem Mathematischen Seminarder Universitat Hamburg, 21, 63-77. [Google Scholar] [CrossRef] 
[4] Graham, R.I. and Pollak, H.O. (1972) On Embedding Graphs in Squashed Cube. Graph Theory and Applications, 303, 99-110. [Google Scholar] [CrossRef] 
[5] Cheng, B. and Liu, B.L. (2007) On the Nullity of Graphs. Linear Algebra and its Applications, 16, 60-67. [Google Scholar] [CrossRef] 
[6] Fan, Y.Z. and Qian, K.S. (2009) On the Nullity of Bipartite Graphs. Linear Algebra and its Applications, 430, 2943-2949. [Google Scholar] [CrossRef] 
[7] Guo, J.M., Yan, W. and Yeh, Y.N. (2009) The Nullity and Matching Number of Unicyclic Graphs. Linear Algebra and its Applications, 431, 1293-1301. [Google Scholar] [CrossRef] 
[8] Fan, Y.Z., Wang, Y. and Wang, Y. (2013) A Note on the Nullity of Unicyclic Signed Graphs. Linear Algebra and its Applications, 438, 1193-1200. [Google Scholar] [CrossRef] 
[9] Yu, G.H., Feng, L.H. and Wang, Q.W. (2013) Bicyclic Graphs with Small Positive Index of Inertia. Linear Algebra and its Applications, 438, 2036-2045. [Google Scholar] [CrossRef] 
[10] 孟霞飞, 马海成, 李生刚. 两类三圈图的正负惯性指数和零度[J]. 陕西师范大学学报(自然科学版), 2013(4): 16-19.
[11] 杨陈, 马海成. 两类特殊三圈图的正负惯性指数和零度[J]. 山东大学学报(理学版), 2015(2): 32-37.

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