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ISRN Discrete Mathematics

Volume 2011 (2011), Article ID 108509, 21 pages

http://dx.doi.org/10.5402/2011/108509

Research Article

## On the Spectrum of Threshold Graphs

Mathematics Department, Faculty of Science, University of Malta, Msida MSD 2080, Malta

Received 29 September 2011; Accepted 3 November 2011

Academic Editors: F. Ergun, P. Feinsilver, Y. Hou, S. Y. Song, and N. I. Trinajstić

Copyright © 2011 Irene Sciriha and Stephanie Farrugia. 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.

#### Linked References

- I. Sciriha and I. Gutman, “Nut graphs: maximally extending cores,”
*Utilitas Mathematica*, vol. 54, pp. 257–272, 1998. View at Google Scholar · View at Zentralblatt MATH - F. R. Gantmacher II,
*The Theory of Matrices*, Chelsea, New York, NY, USA, 1960. - V. Chvátal and P. L. Hammer, “Aggregation of inequalities in integer programming,” in
*Studies in Integer Programming (Proc. Workshop, Bonn, 1975)*, P. L. Hammer, E. L. Johnson, B. H. Korte, et al., Eds., Annals of Discrete Mathematics, 1, pp. 145–162, North-Holland, Amsterdam, The Netherlands, 1977. View at Google Scholar · View at Zentralblatt MATH - P. B. Henderson and Y. Zalcstein, “A graph-theoretic characterization of the PV class of synchronizing primitives,”
*SIAM Journal on Computing*, vol. 6, no. 1, pp. 88–108, 1977. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. C. Golumbic,
*Algorithmic Graph Theory and Perfect Graphs*, vol. 57 of*Annals of Discrete Mathematics*, Elsevier Science, Amsterdam, The Netherlands, 2nd edition, 2004. - N. V. R. Mahadev and U. N. Peled,
*Threshold Graphs and Related Topics*, vol. 56 of*Annals of Discrete Mathematics*, North-Holland, Amsterdam, The Netherlands, 1995. - R. Merris,
*Graph Theory*, Wiley-Interscience Series in Discrete Mathematics and Optimization, Wiley-Interscience, New York, NY, USA, 2001. - A. Brandstädt, V. B. Le, and J. P. Spinrad,
*Graph Classes: A Survey*, SIAM Monographs on Discrete Mathematics and Applications, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1999. - H. A. Jung, “On a class of posets and the corresponding comparability graphs,”
*Journal of Combinatorial Theory. Series B*, vol. 24, no. 2, pp. 125–133, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - H. Lerchs, “On cliques and kernels,” Tech. Rep., Department of Computer Science, University of Toronto, 1971. View at Google Scholar
- D. Seinsche, “On a property of the class of
*n*-colorable graphs,”*Journal of Combinatorial Theory. Series B*, vol. 16, pp. 191–193, 1974. View at Publisher · View at Google Scholar - D. P. Sumner, “Dacey graphs,”
*Journal of the Australian Mathematical Society*, vol. 18, pp. 492–502, 1974. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - T. Biyikoglu, S. K. Simi, and Z. Stanić, “Some notes on spectra of cographs,”
*Ars Combinatoria*, vol. 100, pp. 421–434, 2011. View at Google Scholar - D. G. Corneil, Y. Perl, and L. K. Stewart, “A linear recognition algorithm for cographs,”
*SIAM Journal on Computing*, vol. 14, no. 4, pp. 926–934, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - E. Ruch and I. Gutman, “The branching extent of graphs,”
*Journal of Combinatorics, Information & System Sciences*, vol. 4, no. 4, pp. 285–295, 1979. View at Google Scholar · View at Zentralblatt MATH - R. A. Brualdi and A. J. Hoffman, “On the spectral radius of (0, 1)-matrices,”
*Linear Algebra and Its Applications*, vol. 65, pp. 133–146, 1985. View at Publisher · View at Google Scholar - R. A. Brualdi and E. S. Solheid, “On the spectral radius of connected graphs,”
*Institut Mathématique. Publications. Nouvelle Série*, vol. 39(53), pp. 45–54, 1986. View at Google Scholar · View at Zentralblatt MATH - Z. Stanić, “On nested split graphs whose second largest eigenvalue is less than 1,”
*Linear Algebra and Its Applications*, vol. 430, no. 8-9, pp. 2200–2211, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - I. Sciriha, “A characterization of singular graphs,”
*Electronic Journal of Linear Algebra*, vol. 16, pp. 451–462, 2007. View at Google Scholar · View at Zentralblatt MATH - I. Sciriha, “On the rank of graphs,” in
*Combinatorics, Graph Theory, and Algorithms*, Y. Alavi, D. R. Lick, and A. Schwenk, Eds., vol. 2, pp. 769–778, New Issues Press, Kalamazoo, Mich, USA, 1999. View at Google Scholar - I. Sciriha, “On the construction of graphs of nullity one,”
*Discrete Mathematics*, vol. 181, no. 1–3, pp. 193–211, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - I. Sciriha, S. Fiorini, and J. Lauri, “Minimal basis for a vector space with an application to singular graphs,”
*Graph Theory Notes of New York*, vol. 31, pp. 21–24, 1996. View at Google Scholar - I. Sciriha, “Maximal core size in singular graphs,”
*Ars Mathematica Contemporanea*, vol. 2, no. 2, pp. 217–229, 2009. View at Google Scholar · View at Zentralblatt MATH - G. F. Royle, “The rank of a cograph,”
*The Electronic Journal of Combinatorics*, vol. 10, no. 1, 2003. View at Google Scholar · View at Zentralblatt MATH - D. Cvetković and M. Petrić, “A table of connected graphs on six vertices,”
*Discrete Mathematics*, vol. 50, no. 1, pp. 37–49, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - E. M. Hagos, “Some results on graph spectra,”
*Linear Algebra and Its Applications*, vol. 356, pp. 103–111, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - I. Sciriha and D. M. Cardoso, “Necessary and sufficient conditions for a hamiltonian graph,”
*Journal of Combinatorial Mathematics and Combinatorial Computing*. In press. - D. M. Cvetković, M. Doob, and H. Sachs,
*Spectra of Graphs*, Johann Ambrosius Barth, Heidelberg, Germany, 3rd edition, 1995. - R. Merris, “Antiregular graphs are universal for trees,”
*Univerzitet u Beogradu. Publikacije Elektrotehničkog Fakulteta. Serija Matematika*, vol. 14, pp. 1–3, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - R. B. Bapat,
*Graphs and Matrice*, Hindustan Book Agency, New Delhi, India, 2011. - H. Bai, “The Grone-Merris conjecture,”
*Transactions of the American Mathematical Society*, vol. 363, no. 8, pp. 4463–4474, 2011. View at Publisher · View at Google Scholar