《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (11): 160-164.doi: 10.6040/j.issn.1671-9352.0.2022.011
摘要:
用符号Γn表示点数为n、负惯性指数为2的所有图构成的图集。利用定义的图的3种合同变换, 在图集Γn中可以找出8个零度不超过2的特殊的图, 使得图集Γn中其它图都可以由这8个特殊的图构造出来。因此, 负惯性指数为2的图得到了完整的刻画。
中图分类号:
1 | FAN Yizheng , QIAN Keshi . On the nullity of bipartite graphs[J]. Linear Algebra & its Applications, 2009, 430, 2943- 2949. |
2 | MA Haicheng , YANG Wenhua , LI Shenggang . Positive and negative inertia index of a graph[J]. Linear Algebra & its Applications, 2013, 438, 331- 341. |
3 |
OBOUDI M R . Bipartite graphs with at most six non-zero eigenvalues[J]. ARS Mathematica Contemporenea, 2016, 11, 315- 325.
doi: 10.26493/1855-3974.749.264 |
4 | OBOUDI M R . Characterization of graphs with exactly two non-negative eigen-values[J]. ARS Mathematica Contemporenea, 2017, 12, 271- 286. |
5 | SMITH J H . Symmetry and multiple eigenvalues of graphs[J]. Glasnik Mat Ser Ⅲ, 1977, 12 (1): 3- 8. |
6 |
DUAN Fang , HUANG Qiongxiang , HUANG Xueyi . On graphs with exactly two positive eigenvalues[J]. ARS Mathematica Contemporenea, 2019, 17, 319- 347.
doi: 10.26493/1855-3974.1516.58f |
7 |
DUAN Fang , HUANG Qiongxiang , HUANG Xueyi , et al. A complete characterization of graphs with exactly two positive eigenvalues[J]. Advances in Applied Mathematics, 2023, 144, 102457.
doi: 10.1016/j.aam.2022.102457 |
8 |
TORGAŠEV A . Graphs with exactly two negative eigenvalues[J]. Math Nachr, 1985, 122, 135- 140.
doi: 10.1002/mana.19851220113 |
9 |
TORGAŠEV A . On graphs with a fixed number of negative eigenvalues[J]. Discrete Mathematics, 1985, 57, 311- 317.
doi: 10.1016/0012-365X(85)90184-0 |
10 | CVETKOVIĆD , DOOB M , SACH H . Spectra of graphs: theory and application[M]. New York: Academic Press, 1980: 81- 103. |
[1] | 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, 50(02): 32-37. |
|