In the paper, we give a necessary and
sufficient condition of matching equivalence of two graphs with the maximum
matching root less than or equal to 2.
References
[1]
Farrell, E.J. (1979) An Introduction to Matching Polynomial. Journal of Combinatorial Theory, 27, 75-86.
http://dx.doi.org/10.1016/0095-8956(79)90070-4
[2]
Godsil, C.D. and Gutman, I. (1981) On the Theory of the Matching Polynomials. Journal of Graph Theory, 5, 79-87.
http://dx.doi.org/10.1002/jgt.3190050203
[3]
Beezer, R.A. and Farrell, E.J. (1995) The Matching Polynomials of a Regular Graph. Discrete Mathematics, 137, 7-8.
http://dx.doi.org/10.1016/0012-365X(93)E0125-N
[4]
Farrell, E.J. and Whitehead Jr., E.G. (1992) Connections between the Matching and Chromatic Polynomials. International Journal of Mathematics and Mathematical Sciences, 15, 757-766.
http://dx.doi.org/10.1155/S016117129200098X
[5]
Farrell, E.J. and Guo, J.M. (1993) On the Characterizing Properties of Matching Polynomials. Vishwa International Journal of Graph Theory, 2, 55-62.
[6]
Farrell, E.J., Guo, J.M. and Constantine, G.M. (1991) On Matching Coefficents. Discrete Mathematics, 89, 203-210.
http://dx.doi.org/10.1016/0012-365X(91)90369-D
[7]
Godsil, C.D. (1993) Algebraic Combinatorics. Chapman and Hall, New York.
[8]
Godsil, C.D. (1981) Hermite Polynomiala and a Duality Relation for Matching Polynomials. Combinnatorica, 1, 257- 262. http://dx.doi.org/10.1007/BF02579331
[9]
Godsil, C.D. and Gutman, I. (1981) Some Remarks on the Matching Polynomial and Its Zeros. Croatica Chemica Acta, 54, 53-59.
[10]
Heilmann, O.J. and Lieb, E.H. (1972) Theory of Monomer-Dimer Systems. Communications in Mathematical Physics, 25, 190-232. http://dx.doi.org/10.1007/BF01877590
[11]
Ma, H.C. and Xia, H. (2001) The Graph with Matching Polynomials Maximum Roots of no Excess 2. Journal of Jilin Institute of Chemical Technology, 18, 67-68. (In Chinese)
[12]
Ma, H.C. (2000) On the Matching Equivalent Classes of Two Kind of Graphs. Journal of Mathematical Study, 33, 218- 222. (In Chinese)
[13]
Ma, H.C. (2002) The Matching Equivalent Classes of Graphs of I Shape. Journal of Mathematical Study, 35, 65-71. (In Chinese)
[14]
Cvetkovic, D.M., Doob, M. and Sachs, H. (1995) Spectra of Graphs. 3rd Edition, Johann Abrosius Barth Verlag.
