-cospectrality and -energy in cographs

References

• Balaban AT, Ciubotariu D, Medeleanu M. Topological indices and real number vertex invariants based on graph eigenvalues and eigenvectors. J Chem Inf Comput Sci. 1991;31:517–523.
   Google Scholar
• Dobrynin AA, Entringer R, Gutman I. Wiener index of trees: theory and applications. Acta Appl Math: Int Surv J Appl Math Mathematical Appl. 2001;66(3):211–249.
   Google Scholar
• Graham RL, Pollak HO. On the addressing problem for loop switching. Bell Syst Tech J. 1971;50:2495–2519.
   Google Scholar
• Aouchiche M, Hansen P. Two Laplacians for the distance matrix of a graph. Linear Algebra Appl. 2013;439:21–33.
   Web of Science ®Google Scholar
• Xing R, Zhou B. On the distance and distance signless Laplacian spectral radii of bicyclic graphs. Linear Algebra Appl. 2013;439:3955–3963.
   Web of Science ®Google Scholar
• Corneil DG, Lerchs H, Stewart L. Bhirmingham. Complement reducible graphs, Discrete Appl Math. 1981;3:163–174.
   Web of Science ®Google Scholar
• Nakano K, Olariu S, Zomaya A. A time-optimal solution for the path cover problem on cographs. Theoret Comput Sci. 2003;290:1541–1556.
   Web of Science ®Google Scholar
• Gagneur J, Krause R, Bouwmeester T, et al. Modular decomposition of protein-protein interaction networks. Genome Biol. 2004;5:R57.
   PubMed Web of Science ®Google Scholar
• Corneil DG, Perl Y, Stewart L. Birmingham. A linear recognition algorithm for cographs, SIAM Journal on Computing. 1985;14(4):926–934.
   Web of Science ®Google Scholar
• Habib M, Paul C. A simple linear time algorithm for cograph recognition graphs. Discrete Appl Math. 2005;145(2):183–197.
   Web of Science ®Google Scholar
• Sciriha I, Farrugia S. On the spectrum of threshold graphs. ISRN Discrete Math. 2011;2011:21. Doi:10.5402/2011/108509.
   Google Scholar
• Jacobs DP, Trevisan V, Tura F. Eigenvalue location in threshold graphs. Linear Algebra Appl. 2013;439:2762–2773.
   Web of Science ®Google Scholar
• Jacobs DP, Trevisan V, Tura F. Eigenvalues and energy in threshold graphs. Linear Algebra Appl. 2015;465:412–425.
   Web of Science ®Google Scholar
• Mohammadian A, Trevisan V. Some spectral properties of cographs. Discrete Appl Math. 2016;339:1261–1264.
   Google Scholar
• Hammer PL, Kelmans AK. Laplacian spectra and spanning trees of threshold graphs. Discrete Appl Math. 1996;65:255–273.
   Web of Science ®Google Scholar
• Sillke T. Graphs with maximal ranks, 2001. Available from: https://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/cograph.
   Google Scholar
• Royle GF. The rank of cographs. J Comb. 2003;10(1):7p. Research paper No. 11.
   Google Scholar
• Bıyıkoğlu T, Simić SK, Stanić Z. Some notes on spectra of cographs. Ars Combinatoria. 2011;100:421–434.
   Web of Science ®Google Scholar
• Huang LH, Tam BS, Wu SH. Graphs whose adjacency matrices have rank equal to the number of distinct nonzero rows. Linear Algebra Appl. 2013;438:4008–4040.
   Web of Science ®Google Scholar
• Sander T. On certain eigenspaces of cographs. Electron J Comb. 2003;10: Note 11.
   Google Scholar
• Godsil CD, McKay BD. Constructing cospectral graphs. Aequationes Math. 1982;25(2–3):257–268.
   Google Scholar
• Hammer WH, Spence E. Enumeration of cospectral graphs. European J Combinatorics. 2004;25(2):199–211.
   Web of Science ®Google Scholar
• Schwenk AJ. Almost all trees are cospectral. New directions in the theory of graphs (Proceedings of the Third Ann Arbor Conference on University of Michigan, Ann Arbor, MI, 1971). New York (NY): Academic Press; 1973. p. 275–307.
   Google Scholar
• Mckay BD. On the spectral characterization of trees. Ars Combinatoria. 1977;3:219–232.
   Google Scholar
• Carvalho J, Souza BS, Trevisan V, et al. Exponentially many graphs have a Q-cospectral mate. Manuscript submitted for publication. 2016.
   Google Scholar
• Cvetković DM, Doob M, Sachs H. Spectra of graph. Theory and application, New York (NY): Academic Press Inc.; 1980.
   Google Scholar
• Fritscher E, Trevisan V. Exploring symmetries to decompose matrices and graphs preserving the spectrum. SIAM J Matrix Anal Appl. 2016;37:260–289.
   Web of Science ®Google Scholar
• Li X, Shi Y, Gutman I. Graph energy. New York (NY): Springer; 2012.
   Google Scholar
• Hou Y, Tao Q. Borderenergetic threshold graphs. MATCH Commun Math Comput Chem. 2016;75:253–262.
   Web of Science ®Google Scholar