On the nullity of the line graph of unicyclic graph with depth one

Linear Algebra and Its Applications

Volumn 437, Issue 8, 2012, Pages 2038-2055

  Li, Hong Hai ^a   Fan, Yi Zheng ^b   Su, Li ^a  

^a JIANGXI NORMAL UNIVERSITY   (China)

^b ANHUI UNIVERSITY   (China)

Author keywords

Line graph; Nullity; Rank; Unicyclic graph

Indexed keywords

CONNECTED GRAPH; LINE GRAPH; NULLITY; RANK; UNICYCLIC GRAPH;

LINEAR ALGEBRA; MATHEMATICAL TECHNIQUES;

GRAPH THEORY;

EID: 84864430363     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2012.05.028     Document Type: Article

References (29)

1. F. Ashraf, and H. Bamdad A note on graphs with zero nullity Match 60 2008 15 19
2. G.J. Chang, L.-H. Huang, and H.-G. Yeh A characterization of graphs with rank 4 Linear Algebra Appl. 434 2011 1793 1798
3. G.J. Chang, L.-H. Huang, and H.-G. Yeh A characterization of graphs with rank 5 Linear Algebra Appl. 436 2012 4241 4250
4. B. Cheng, and B.L. Liu On the nullity of unicyclic graphs Electron. J. Linear Algebra 16 2007 60 67
5. L. Collatz, and U. Sinogowitz Spectren endlicher grafen Abh. Math. Sem. Univ. Hamburg. 21 1957 63 77
6. D. Cvetković, and I. Gutman The algebraic multiplicity of the number zero in the spectrum of a bipartite graph Mat. Vesnik. 9 1972 141 150
7. D.M. Cvetković, M. Doob, and H. Sachs Spectra of Graphs 1980 Academic Press New York
8. D. Cvetković, P. Rowlinson, and S.K. Simić Signless Laplacians of finite graphs Linear Algebra Appl. 423 2007 155 171 (Pubitemid 46415757)
9. D. Cvetković, P. Rowlinson, and S.K. Simić Eigenvalue bounds for the signless Laplacian Publ. Inst. Math. (Beograd) 81 95 2007 11 27
10. D. Cvetković, P. Rowlinson, and S.K. Simić Spectral Generalizations of Line Graphs: On Graphs with Least Eigenvalue - 2 2004 Cambridge University Press Cambridge
11. Y.Z. Fan, and K.S. Qian On the nullity of bipartite graphs Linear Algebra Appl. 430 2009 2943 2949
12. S. Fiorini, I. Gutman, and I. Sciriha Trees with maximum nullity Linear Algebra Appl. 397 2005 245 251 (Pubitemid 40146323)
13. S.C. Gong, Y.Z. Fan, and Z.X. Yin On the nullity of graphs with pendant trees Linear Algebra Appl. 433 2010 1374 1380
14. S.C. Gong, and G.H. Xu On the nullity of a graph with cut-points Linear Algebra Appl. 436 2012 135 142
15. J.M. Guo, W.G. Yan, and Y.N. Yeh On the nullity and the matching number of unicyclic graphs Linear Algebra Appl. 431 2009 1293 1301
16. I. Gutman, and I. Sciriha On the nullity of line graphs of trees Discrete Math. 232 2001 35 45 (Pubitemid 33660369)
17. R.A. Horn, and C.R. Johnson Matrix Analysis 1985 Cambridge University Press
18. S.B. Hu, X.Z. Tan, and B.L. Liu On the nullity of bicyclic graphs Linear Algebra Appl. 429 2008 1387 1391
19. A.Ya. Khinchin Continued Fractions 1964 University of Chicago Press (Originally published in Russian, 1935)
20. S.C. Li On the nullity of graphs with pendent vertices Linear Algebra Appl. 429 2008 1619 1628
21. H.H. Li, L. Su, and H.X. Sun On bipartite graphs which attain minimum rank among bipartite graphs with a given diameter Electron. J. Linear Algebra 23 2012 137 150
22. W. Li, and A. Chang On the trees with maximum nullity Match 56 2006 501 508
23. H.C. Longuet-Higgins Resonance structures and MO in unsaturated hydrocarbons J. Chem. Phys. 18 1950 265 274
24. J.X. Li, A. Chang, and W.C. Shiu On the nullity of bicyclic graphs Match 60 2008 21 36
25. M. Nath, and B.K. Sarma On the null-spaces of acyclic and unicyclic singular graphs Linear Algebra Appl. 427 2007 42 54
26. G.R. Omidi On the nullity of bipartite graphs Graphs Combin. 25 2009 111 114
27. A.J. Schwenk Computing the characteristic polynomial of a graph R.A. Bari, F. Harary, Graphs and Combinatorics, Lecture Notes in Mathematics vol. 406 1974 Springer-Verlag New York 153 173
28. X.Z. Tan, and B.L. Liu On the nullity of unicyclic graphs Linear Algebra Appl. 408 2005 212 220
29. B. Zhou, and I. Gutman A connection between ordinary and Laplacian spectra of bipartite graphs Linear and Multilinear Algebra 56 2008 305 310