In the paper, We discussed the matching uniqueness of graphs with degree sequence . The necessary and sufficient conditions for and its complement are matching unique are given.
References
[1]
Godsil, C.D. (1993) Algebraic Combinatorics. Chapman and Hall, New York, London.
[2]
Shen, S.C. (2001) A Necessary and Sufficient Conditions for Matching Uniqueness of a Class of T-Shape tree. Journal of Mathematical Study, 34, 411-416.
[3]
Ma, H.C. (2003) The Matching Equivalent Classes of Graphs with the Maximum Root Less than 2. Journal of Systems Science and Mathematical Sciences, 3, 337-342.
[4]
Cvetkovic, D.M., Doob, M. and Sachs, H. (1980) Spectra of Graphs. Academic Press, New York.
[5]
Ghareghani, N., Omidi, G.R. and Tayfeh-Rezaie, B. (2007) Spectral Characterization of Graphs with Index at Most√2 +√5 . Linear Algebra and Its Applications, 420, 483-489. http://dx.doi.org/10.1016/j.laa.2006.08.009
[6]
Beezet, R.A. and Farrell, E.J. (1995) The Matching Polynomials of a Regular Graphs. Discrete Mathematics, 137, 7-18.
![\"\"](\"Edit_06119116-a5ba-4680-a6ad-dd7b46d7dcc2.bmp\")
. The necessary and sufficient conditions for![\"\"](\"Edit_fe63ee06-2169-4f1a-b031-30037e0d77ad.bmp\")
and its complement are matching unique are given.
