The inertia of weighted unicyclic graphs

Linear Algebra and Its Applications

Volumn 448, Issue , 2014, Pages 130-152

  Yu, Guihai ^a,b   Zhang, Xiao Dong ^c   Feng, Lihua ^d  

^a SHANDONG INSTITUTE OF BUSINESS AND TECHNOLOGY   (China)

^b NANKAI UNIVERSITY   (China)

^c SHANGHAI JIAO TONG UNIVERSITY   (China)

^d CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

Adjacency matrix; Inertia; Weighted unicyclic graphs

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

ADJACENCY MATRICES; EIGENVALUES; INERTIA; LOWER BOUNDS; NEGATIVE INDEX; UNICYCLIC GRAPH; WEIGHTED GRAPH;

GRAPHIC METHODS;

EID: 84897513724     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2014.01.023     Document Type: Article

References (27)

1. A. Berman, and M. Farber A lower bound for the second largest Laplacian eigenvalues of weighted graphs Electron. J. Linear Algebra 22 2011 1179 1184
2. B. Borovićanin, and I. Gutman Nullity of graphs D. Cvetković, I. Gutman, Applications of Graph Spectra 2009 Math. Inst. Belgrade 107 122
3. B. Cheng, and B.L. Liu On the nullity of graphs Electron. J. Linear Algebra 16 2007 60 67
4. G.J. Chang, L.H. Huang, and H.G. Yeh A characterization of graphs with rank 4 Linear Algebra Appl. 434 8 2011 1793 1798
5. G.J. Chang, L.H. Huang, and H.G. Yeh A characterization of graphs with rank 5 Linear Algebra Appl. 436 11 2012 4241 4250
6. L. Collatz, and U. Sinogowitz Spektren endlicher Grafen Abh. Math. Semin. Univ. Hambg. 21 1957 63 77
7. D.M. Cvetković, and I.M. Gutman The algebraic multiplicity of the number zero in the spectrum of a bipartite graph Mat. Vesnik 9 24 1972 141 150
8. D. Cvetković, and P. Rowlinson Spectra of unicyclic graphs Graphs Combin. 3 1978 7 23
9. K.C. Das Extremal graph characterization from the bounds of the spectral radius of weighted graphs Appl. Math. Comput. 217 2011 7420 7426
10. K.C. Das, and R.B. Bapat A sharp upper bound on the spectral radius of weighted graphs Discrete Math. 308 2008 3180 3186 (Pubitemid 351657505)
11. S. Daugherty The inertia of unicyclic graphs and the implications for closed-shells Linear Algebra Appl. 429 2008 849 858
12. Y.Z. Fan, W. Du, and C. Dong The nullity of bicyclic signed graphs arXiv:1207.6765v1
13. Y.Z. Fan, Y. Wang, and Y. Wang A note on the nullity of unicyclic signed graphs Linear Algebra Appl. 438 2013 1193 1200
14. P.W. Fowler, and D.E. Manolopoulos An Atlas of Fullerenes 1995 Clarendon Press Oxford
15. S.C. Gong, Y.Z. Fan, and Z. Yin On the nullity of graphs with pendant trees Linear Algebra Appl. 433 2010 1374 1380
16. D.A. Gregory, B. Heyink, and K.N. Vander Meulen Inertia and biclique decompositions of joins of graphs J. Combin. Theory Ser. B 88 2003 135 151 (Pubitemid 36593538)
17. D.A. Gregory, V.L. Watts, and B.L. Shader Biclique decompositions and Hermitian rank Linear Algebra Appl. 292 1999 267 280 (Pubitemid 129563065)
18. J. Guo, W. Yan, and Y. Yeh On the nullity and the matching number of unicyclic graphs Linear Algebra Appl. 431 2009 1293 1301
19. I. Gutman, and N. Trinajstić Graph theory and molecular orbitals Top. Curr. Chem. 42 1973 49 93
20. R.A. Horn, and C.R. Johnson Matrix Analysis second ed. 2012 Cambridge University Press
21. H.C. Longuet-Higgins Some studies in molecular orbital theory I. Resonance structures and molecular orbitals in unsaturated hydrocarbons J. Chem. Phys. 18 1950 265 274
22. H.C. Ma, W.H. Yang, and S.G. Li Positive and negative inertia index of a graph Linear Algebra Appl. 438 2013 331 341
23. I. Sciriha On the rank of graphs Y. Alavi, D.R. Lick, A. Schwenk, Combinatorics, Graph Theory, and Algorithms, vol. II 1999 New Issue Press, Western Michigan University Kalamazoo, MI 769 778
24. S. Sorgun, and Ş. Büyükköse On the bounds for the largest Laplacian eigenvalues of weighted graphs Discrete Optim. 9 2012 122 129
25. S. Sorgun, and Ş. Büyükköse The new upper bounds on the spectral radius of weighted graphs Appl. Math. Comput. 218 2012 5231 5238
26. X. Tan, and B. Liu On the nullity of unicyclic graphs Linear Algebra Appl. 408 2005 212 220 (Pubitemid 41260480)
27. G. Yu, L. Feng, and Q. Wang Bicyclic graphs with small positive index of inertia Linear Algebra Appl. 438 2013 2036 2045