Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 105624, 4 pages
Signless Laplacian Polynomial and Characteristic Polynomial of a Graph
1Department of Mathematics, Gogte Institute of Technology, Udyambag, Belgaum 590008, India
2Department of Mathematics, B.V.Bhoomaraddi College of Engineering & Technology, Hubli 580031, India
Received 21 July 2012; Accepted 6 September 2012
Academic Editor: Kinkar C. Das
Copyright © 2013 Harishchandra S. Ramane et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. Li, “Some lower bounds for Laplacian energy of graphs,” International Journal of Contemporary Mathematical Sciences, vol. 4, no. 5, pp. 219–223, 2009.
- Z. Liu, “Energy, Laplacian energy and Zagreb index of line graph, middle graph and total graph,” International Journal of Contemporary Mathematical Sciences, vol. 5, no. 18, pp. 895–900, 2010.
- B. Mohar, “The Laplacian spectrum of graphs,” in Graph Theory, Combinatorics and Applications, Y. Alavi, G. Chartrand, O. E. Ollerman, and A. J. Schwenk, Eds., pp. 871–898, John Wiley & Sons, New York, NY, USA, 1991.
- B. Mohar, “Graph laplacians,” in Topics in Algebraic Graph Theory, L. W. Beineke and R. J. Wilson, Eds., pp. 113–136, Cambridge University Press, Cambridge, UK, 2004.
- D. Cvetković, “Signless Laplacians and line graphs,” Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences Mathématiques Naturelles/Sciences Mathematiques, vol. 131, no. 30, pp. 85–92, 2005.
- D. Cvetković, P. Rowlinson, and S. K. Simić, “Signless Laplacians of finite graphs,” Linear Algebra and Its Applications, vol. 423, no. 1, pp. 155–171, 2007.
- D. Cvetković, P. Rowlinson, S. K. Simic, and S. K. Simić, “Eigenvalue bounds for the signless Laplacian,” Publications de l'Institut Mathématique, vol. 81, no. 95, pp. 11–27, 2007.
- D. Cvetković, P. Rowlinson, and S. Simić, An Introduction to the Theory of Graph Spectra, Cambridge Univeristy Press, Cambridge, UK, 2010.
- A. Daneshgar and H. Hajiabolhassan, “Graph homomorphisms and nodal domains,” Linear Algebra and Its Applications, vol. 418, no. 1, pp. 44–52, 2006.
- L. Feng and G. Yu, “On three conjectures involving the signless Laplacian spectral radius of graphs,” Publications de l'Institut Mathematique, vol. 85, no. 99, pp. 35–38, 2009.
- W. H. Haemers and E. Spence, “Enumeration of cospectral graphs,” European Journal of Combinatorics, vol. 25, no. 2, pp. 199–211, 2004.
- E. R. van Dam and W. H. Haemers, “Which graphs are determined by their spectrum?” Linear Algebra and Its Applications, vol. 373, pp. 241–272, 2003.
- H. B. Walikar and H. S. Ramane, “Laplacian polynomial and number of spanning trees in terms of characteristic polynomial of induced subgraphs,” AKCE International Journal of Graphs and Combinatorics, vol. 5, no. 1, pp. 35–48, 2008.
- F. Harary, Graph Theory, Narosa Publishing House, New Delhi, India, 1998.
- H. S. Ramane, Some topics in spectral graph theory [Ph.D. thesis], Karnatak University, Dharwad, India, 2002.
- D. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs, Academic Press, New York, NY, USA, 1980.
- H. Sachs, “Über Teiler, Faktoren und charakteristische Polynome von Graphen,” Teil I. Wiss. Z. TH Ilmenau, vol. 13, pp. 405–412, 1967.
- D. Cvetković, “Spectra of graphs formed by some unary operations,” Publications De L’Institut Mathe'Matique, vol. 19, no. 33, pp. 37–41, 1975.