ON THE NULLITY OF CONNECTED GRAPHS WITH LEAST EIGENVALUE AT LEAST-2

被引：6

作者：

Zhou, Jiang ^{[1
]}

Sun, Lizhu ^{[1
]}

Yao, Hongmei ^{[1
]}

Bu, Changjiang ^{[1
]}

机构：

[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Peoples R China

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2013年 / 7卷 / 02期

关键词：

Nullity; generalized line graph; adjacency matrix; signless Laplacian matrix; LINE GRAPHS; MAXIMUM NULLITY; STARLIKE TREES;

D O I：

10.2298/AADM130710014Z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let L (resp. L+) be the set of connected graphs with least adjacency eigenvalue at least -2 (resp. larger than -2). The nullity of a graph G, denoted by eta(G), is the multiplicity of zero as an eigenvalue of the adjacency matrix of G. In this paper, we give the nullity set of L+ and an upper bound on the nullity of exceptional graphs. An expression for the nullity of generalized line graphs is given. For G is an element of L, if eta(G) is sufficiently large, then G is a proper generalized line graph (G is not a line graph).

引用

页码：250 / 261

页数：12

共 28 条

[1]

Ashraf F, 2008, MATCH-COMMUN MATH CO, V60, P15

[2]

Bapat R.B., 2011, B KERALA MATH ASS, V8, P207

[3] Starlike trees whose maximum degree exceed 4 are determined by their Q-spectra [J].

Bu, Changjiang ;

Zhou, Jiang .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (01) :143-151

[4] LINE GRAPHS, ROOT SYSTEMS, AND ELLIPTIC GEOMETRY [J].

CAMERON, PJ ;

GOETHALS, JM ;

SEIDEL, JJ ;

SHULT, EE .

JOURNAL OF ALGEBRA, 1976, 43 (01) :305-327

[5]

Collatz L., 1957, Abh. Math. Semin. Univ. Hamburg, V21, P63, DOI DOI 10.1007/BF02941924

[6] GENERALIZED LINE GRAPHS [J].

CVETKOVIC, D ;

DOOB, M ;

SIMIC, S .

JOURNAL OF GRAPH THEORY, 1981, 5 (04) :385-399

[7] Graphs with least eigenvalue - 2: The star complement technique [J].

Cvetkovic, D ;

Rowlinson, P ;

Simic, SK .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2001, 14 (01) :5-16

[8]

Cvetkovic D, 2010, An Introduction to the Theory of Graph Spectra

[9]

Cvetkovic D., 2004, Spectral Generalizations of Line Graphs. On Graphs with Least Eigenvalue -2

[10] COSPECTRAL GRAPHS WITH LEAST EIGENVALUE AT LEAST-2 [J].

Cvetkovic, Dragos ;

Lepovic, Mirko .

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2005, 78 (92) :51-63

← 1 2 3 →