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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (2): 134-137    DOI: 10.3785/j.issn.1008-9497.2016.02.002
数学与计算机科学     
几个图运算下的图的惯性指数的界
曲慧1, 刘伟俊2,3
1. 山东工商学院数学学院, 山东烟台 264005;
2. 中南大学数学学院, 湖南长沙 410083;
3. 南通大学理学院, 江苏南通 226019
Bounding the inertia of graphs under some graph operations
QU Hui1, LIU Weijun2,3
1. Department of Mathematics, Shandong Institute of Business and Technology, Yantai 264005, Shandong Province, China;
2. Department of Mathematics, Central South University, Changsha 410083, China;
3. School of Science, Nantong University, Nantong 226019, Jiangsu Province, China
 全文: PDF(1125 KB)  
摘要： 图的惯性指数是指三元组In(G)={i+(G),i-(G),i0(G)},其中i+(G),i-(G),i0(G)分别是图的邻接矩阵A(G)的正、负、零特征值的数目(包括重数).得到了包括加一个点、加一条边、剖分一条边、重合2个点、图的联等运算下图的正惯性指数的界.
关键词： 图运算;  邻接矩阵;  惯性指数    
Abstract: The inertia of a graph G is defined to be the triple In(G)={i+(G), i-(G), i0(G)}, where i+(G), i-(G), i0(G) are the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G) including multiplicities, respectively. Some bounds for the positive index of inertia of a graph under some graph operations including adding a vertex or an edge, subdivision of an edge, contracting of two vertices and the join of graphs, are obtained.
Key words: graph operations    adjacency matrix    inertia
收稿日期: 2013-12-26 出版日期: 2016-03-12
CLC:  O157.5  
基金资助: Supported by the Natural Science Foundation of China (11301302, 11101245, 11271208);the Natural Science Foundation of Shandong Province(BS2013SF009).
通讯作者: LIU Weijun, ORCID:http://orcid.org/0000-0003-2396-637X,E-mail:wjliu6210@126.com.     E-mail: wjliu6210@126.com
作者简介: QU Hui(1978-), female, master, lecture, the field of interest is combinatorics.
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引用本文:

曲慧, 刘伟俊. 几个图运算下的图的惯性指数的界[J]. 浙江大学学报（理学版）, 2016, 43(2): 134-137.

QU Hui, LIU Weijun. Bounding the inertia of graphs under some graph operations. Journal of Zhejiang University (Science Edition), 2016, 43(2): 134-137.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.02.002    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I2/134

[1] COLLATZ L, SIGNOGOWITZ U. Spektren endlicher grafen[J]. Abh Math Sere Univ Hamburg,1957,21:63-77.
[2] FIORINI S, GUTMAN I, SCIRIHA I. Trees with maximum nullity[J]. Linear Algebra Appl,2005,397:245-251.
[3] GUO J, YAN W, YEH Y. On the nullity and the matching number of unicyclic graphs[J]. Linear Algebra Appl,2009,431:1293-1301.
[4] LI W, CHANG A. Describing the nonsingular unicyclic graph[J]. J Math Study,2007(4):442-445.
[5] FOWLER P W, MANOLOPOULOS D E. An Atlas of Fullerenes[M]. Oxford:Clarendon Press,1995.
[6] DAUGHERTY S. The inertia of unicyclic graphs and the implications for closed-shells[J]. Linear Algebra Appl,2008,429:849-858.
[7] MA H, YANG W, LI S. Positive and negative inertia index of a graph[J]. Linear Algebra Appl,2013,438:331-341.
[8] YU G, FENG L, WANG Q. Bicyclic graphs with small positive index of inertia[J]. Linear Algebra Appl,2013,438(5):2036-2045.
[9] YU G, FENG L, WANG Q, et al. The minimal positive index of inertia of signed unicyclic graphs[J]. Ars Combin,2014,117:245-255.
[10] YU G, ZHANG X, FENG L. The inertia of weighted unicyclic graphs[J]. Linear Algebra Appl,2014,448:130-152.
[11] FAN Y, QIAN K. On the nullity of bipartite graphs[J]. Linear Algebra Appl,2009,430:2943-2949.
[12] LI W, CHANG A. On the trees with maximum nullity[J]. Match Commum Math Comput Chem,2006,56(3):501-508.
[13] LONGUET-HIGGINS H C. Some studies in molecular orbital theory I. resonance structures and molecular orbitals in unsaturated hydrocarbons[J].J Chem Phys,1950,18:265-274.
[14] NATH M, SARMA B K. On the null-spaces of acyclic and unicyclic graph singular graphs[J].Linear Algebra Appl,2007,427:42-54.
[15] TAN X, LIU B. On the nullity of unicyclic graphs[J].Linear Algebra Appl,2003,408:212-220.
[16] LI J, CHANG A, SHIU W C. On the nullity of bicyclic graphs[J].Match Commum Math Comput Chem,2008,60(1):21-36.
[17] HU S, LIU B, TAN X. On the nullity of bicyclic graphs[J].Linear Algebra Appl,2008,429:1387-1391.
[18] 袁西英,单海英,刘颖.双圈图的零度集合[J]. 同济大学学报:自然科学版,2008,36(3):397-401.
YUAN Xiying, SHAN Haiying, LIU Ying. On the nullity set of bicyclic graphs[J].Journal of Tongji University:Natural Science,2008,36(3):397-401.
[19] CHENG B, LIU B. On the nullity of tricyclic graphs[J].Linear Algebra Appl,2011,434:1799-1810.
[20] GU H.The Nullity of Tricyclic Graphs[D]. Xinjiang:Xinjiang Normal University,2009.
[21] CHENG B, LIU B. On the nullity of graphs[J].Electronic J Linear Algebra,2007,16:60-67.
[22] LIU B, HUANG Y, CHEN S. On the characterization of graphs with pendent vertices and given nullity[J].Electronic J Linear Algebra,2009,18:719-734.
[23] LI S. On the nullity of graphs with pendant vertices[J].Linear Algebra Appl,2008,429:1619-1628.
[24] GONG S, FAN Y, YIN Z. On the nullity of graphs with pendant trees[J].Linear Algebra Appl,2010,433:1374-1380.
[25] HORN R A, JOHNSON C R.Matrix Analysis[M]. Cambridge:Cambridge University Press,1985.
[26] GREGORY D A, HEYINK B, MEULEN K N. Inertia and biclique decompositions of joins of graphs[J].Journal of Comb Theory:Ser B,2003,88:135-151.
[27] HAYNSWORTH E V, OSTROESKI A M. On the inertia of some classes of partitioned matrices[J].Linear Algebra Appl,1968,1(2):299-316.
[28] HAYNSWORTH E V. Determination of the inertia of a partitioned Hermitian matrix[J].Linear Algebra Appl,1968,1(1):73-81.
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