Abstract
We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomials.
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Ayoobi F., Omidi G.R., Tayfeh-Rezaie B.: A note on graphs whose signless Laplacian has three distinct eigenvalues. Linear Multilinear Algebra 59, 701–706 (2011)
Beezer R.A., Farrell E.J.: The matching polynomial of a regular graph. Discrete Math 137, 7–18 (1995)
Bridges W.G., Mena R.A.: Multiplicative cones—a family of three eigenvalue graphs. Aequationes Math 22, 208–214 (1981)
Brouwer A.E., Haemers W.H.: Spectra of Graphs. Springer, Berlin (2012)
van Dam, E.R.: Graphs with Few Eigenvalues. An Interplay between Combinatorics and Algebra. Center Dissertation Series 20, Ph.D. thesis, Tilburg University (1996)
van Dam E.R.: Nonregular graphs with three eigenvalues. J. Comb. Theory Ser. B 73, 101–118 (1998)
van Dam E.R., Haemers W.H.: Graphs with constant μ and \({\bar\mu}\) . Discrete Math 182, 293–307 (1998)
van Dam E.R., Spence E.: Small regular graphs with four eigenvalues. Discrete Math 189, 233–257 (1998)
Doob M.: Graphs with a small number of distinct eigenvalues. Ann NY Acad Sci 175, 104–110 (1970)
Doob M.: On characterizing certain graphs with four eigenvalues by their spectrum. Linear Algebra Appl 3, 461–482 (1970)
Godsil C.D.: Algebraic Combinatorics. Chapman and Hall Mathematics Series. Chapman and Hall, London (1993)
Godsil C.D.: Algebraic matching theory. Electron. J. Combin. 2, #R8 (1995)
Godsil C.D., Gutman I.: On the theory of the matching polynomial. J Graph Theory 5, 137–144 (1981)
Heilmann O.J., Lieb E.H.: Monomers and dimers. Phys. Rev. Lett. 24, 1412–1414 (1970)
Heilmann O.J., Lieb E.H.: Theory of monomer–dimer systems. Comm. Math. Phys. 25, 190–232 (1972)
Klin M., Muzychuk M.: On graphs with three eigenvalues. Discrete Math. 189, 191–207 (1998)
Ku C.Y., Chen W.: An analogue of the Gallai–Edmonds structure theorem for non-zero roots of the matching polynomial. J. Comb. Theory Ser. B 100, 119–127 (2010)
Kunz H.: Location of the zeros of the partition function for some classical lattice systems. Phys. Lett. (A) 32, 311–312 (1970)
Noy M.: Graphs determined by polynomial invariants. Theoret. Comput. Sci. 307, 365–384 (2003)
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Ghorbani, E. Graphs With Few Matching Roots. Graphs and Combinatorics 29, 1377–1389 (2013). https://doi.org/10.1007/s00373-012-1186-7
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DOI: https://doi.org/10.1007/s00373-012-1186-7