Constructing cospectral graphs via a new form of graph product

References

• Cvetković D . Graphs and their spectra (Grafovi i njihovi spektri) [Thesis]. Univ. Beograd Publ. Elektrotehn. Fak., Ser. Mat. Fiz. No. 354--No. 356; 1971. p. 1–50.
   Google Scholar
• Collatz L , Sinogowitz U . Spektren endlicher Grafen. Abh Math Sem Univ Hamburg. 1957;21:63–77.
   Google Scholar
• Schwenk AJ . Almost all trees are cospectral. In: Harary F , editor. New directions in the theory of graphs. New York (NY): Academic Press; 1973. p. 275–307.
   Google Scholar
• van Dam ER , Haemers WH . Which graphs are determined by their spectrum? Linear Algebra Appl. 2003;373:241–272.
   Web of Science ®Google Scholar
• Bollobás B , Pebody L , Riordan O . Contraction--deletion invariants for graphs. J Combin Theory Ser B. 2000;80:320–345.
   Web of Science ®Google Scholar
• Lovász L . Operations with structures. Acta Math Hung. 1967;18:321–328.
   Google Scholar
• Garijo D , Goodall A , Nešetřil J . Distinguishing graphs by their left and right homomorphism profiles. Eur J Comb. 2011;32:1025–1053.
   Web of Science ®Google Scholar
• van Lint JH , Seidel JJ . Equilateral point sets in elliptic geometry. Indag Math. 1966;28:335–348.
   Google Scholar
• Seidel JJ . Graphs and two-graphs. In: Proceedings of the 5th Southeastern Conference on Combinatorics, Graph Theory, and Computing. Boca Raton (FL): Florida Atlantic University; 1974. p. 125–143.
   Google Scholar
• Cvetković D , Doob M , Sachs H . Spectra of graphs. 3rd ed. Johann Abrosius Barth Verlag; 1995; 1st ed., Berlin: Deutscher Verlag der Wissenschaften; 1980; New York (NY): Academic Press; 1980.
   Google Scholar
• Seress Á . Large families of cospectral graphs. Designs Codes Cryptography. 2000;21:205–208.
   Web of Science ®Google Scholar
• Godsil CD , McKay BD . Products of graphs and their spectra. University of Michigan Combinatorial Mathematics IV, Lecture notes in mathematics. 1976;560:61–72.
   Google Scholar
• Godsil CD , McKay BD . Constructing cospectral graphs. Aequationes Math. 1982;25:257–268.
   Google Scholar
• Butler S . Using twins and scaling to construct cospectral graphs for the normalized Laplacian. Electron J Linear Algebra. 2015;28:54–68.
   Web of Science ®Google Scholar
• Butler S , Grout J . A construction of cospectral graphs for the normalized Laplacian. Electron J Comb. 2011;18:P231.
   Web of Science ®Google Scholar
• Levi I , Vilenchik D , Langberg M , et al. Zero vs. ε error in interference channels. IEEE Inf Theory Workshop. 2013;1–5.
   Google Scholar
• Wang W . Generalized spectral characterization of graphs revisited. Electron J Comb. 2013;4.
   Google Scholar
• Wang W , Xu C . A sufficient condition for a family of graphs being determined by their generalized spectra. Eur J Comb. 2006;27:826–840.
   Web of Science ®Google Scholar
• Wang W , Xu C . An excluding algorithm for testing whether a family of graphs are determined by their generalized spectra. Linear Algebra Appl. 2006;418:62–74.
   Web of Science ®Google Scholar
• Weichsel P . The Kronecker product of graphs. Proc Am Math Soc. 1962;13:47–52.
   Google Scholar
• Hedetniemi S . Homomorphisms and graph automata. University of Michigan Technical Report 03105-44-T; 1966.
   Google Scholar
• Garey M , Johnson D . Computers and intractability: a guide to the theory of NP-completeness. New York (NY): W. H. Freeman & Co.; 1979.
   Google Scholar
• Frucht R , Harary F . On the corona of two graphs. Aequationes Math. 1970;4:322–325.
   Google Scholar
• Barik S , Pati S , Sarma BK . The spectrum of the corona of two graphs. SIAM J Discrete Math. 2007;21:47–56.
   Web of Science ®Google Scholar
• Liu X , Zhou S . Spectra of the neighbourhood corona of two graphs. Linear Multilinear Algebra. 2014;62:1205–1219.
   Web of Science ®Google Scholar
• McLeman C , McNicholas E . Spectra of coronae. Linear Algebra Appl. 2011;435:998–1007.
   Web of Science ®Google Scholar
• Šokarovski R . A generalized direct product of graphs. Publications De L’Instituit Mathematique, nouvelle serie. 1977;36:267–269.
   Google Scholar
• Laub A . Matrix analysis for scientists and engineers. Philadelphia (PA): Society for Industrial and Applied Mathematics; 2004.
   Google Scholar
• Alon N , Chung F . Explicit construction of linear sized tolerant networks. Discrete Math. 1988;72:15–19.
   Web of Science ®Google Scholar
• Lovász L , Simonovits M . The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume. In: 31st IEEE Annual Symposium on Foundations of Computer Science; St. Louis (MO); 1990. p. 346–354.
   Google Scholar
• Thomason A . Pseudorandom graphs. Random Graphs ‘85. North-Holland Math Stud. 1987;144:307–31.
   Google Scholar
• Krivelevich M , Sudakov B . Pseudo-random graphs. In: More sets graphs and number. Berlin: Springer-Verlag; 2006. p. 199–262. (Bolyai society mathematical studies; vol. 15).
   Google Scholar
• Vilenchik D . Cospectral graph code. Available from: https://github.com/sdannyvi/cospecral/blob/master/test.m.
   Google Scholar