On Graphs Determined by Their Tutte Polynomials

Graphs and Combinatorics

Volumn 20, Issue 1, 2004, Pages 105-119

  De Mier, Anna ^a   Noy, Marc ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2142838434     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00373-003-0534-z     Document Type: Article

References (24)

1. Ankney, R., Bonin, J.: Characterizations of PG(n - 1, q)/PG(k- 1, q) by numerical and polynomial invariants. Adv. Appl. Math. 28, 287-301 (2002)
2. Asratian, A.S., Denley, T.M.J., Häggkvist, R.: Bipartite graphs and their applications. Cambridge: Cambridge Univ. Press 1998
3. Bollobás, B.: Modern Graph Theory. New York: Springer-Verlag 1998
4. Bollobás, B., Pebody, L., Riordan, O.: Contraction-Deletion Invariants for Graphs. J. Comb. Theory, Ser. B 80, 320-345 (2000)
5. Bonin, J.E.: Strongly inequivalent representations and Tutte polynomials of matroids. Algebra Univers. (to appear)
6. Bonin, J.E., de Mier, A.: T-uniqueness of some families of k-chordal matroids. Adv. Appl. Math. (to appear)
7. Bonin, J.E., Miller, W.P.: Characterizing combinatorial geometries by numerical invariants. Eur. J. Comb. 20, 713-724 (1999)
8. Brylawski, T.: A decomposition for combinatorial geometries. Trans. Am. Math. Soc. 171, 235-282 (1972)
9. Brylawski, T.H.: The Tutte polynomial. Part I: General theory. In: A. Barlotti: Matroid Theory and Its Applications, (C.I.M.E., Liguori, Naples, 1980), 125-175
10. Brylawski, T.: Intersection theory for graphs. J. Comb. Theory, Ser. B 30, 233-246 (1981)
11. Brylawski, T., Oxley, J.: The Tutte Polynomial and its Applications. In: N. White: Matroid Applications, pp. 123-225. Cambridge: Cambridge University Press 1992
12. Koh, K.M., Teo, C.P.: The chromaticity of complete bipartite graphs with at most one edge deleted. J. Graph Theory 14, 89-99 (1990)
13. Koh, K.M., Teo, K.L.: The search for chromatically unique graphs. Graphs Comb. 6, 259-285 (1990)
14. Koh, K.M., Teo, K.L.: The search for chromatically unique graphs II. Discrete Math. 172, 59-78 (1997)
15. van Lint, J.H., Wilson, R.M.: A Course in Combinatorics. Cambridge: Cambridge University Press 1992
16. Márquez, A., de Mier, A., Noy, M., Revuelta, M.P.: Locally grid graphs: classification and Tutte uniqueness. Discrete Math. 266, 327-352 (2003)
17. Merino, C., de Mier, C., Noy, M.: Irreducibility of the Tutte polynomial of a connected matroid. J. Comb. Theory, Ser. B 83, 298-304 (2001)
18. de Mier, A., Noy, M.: Tutte uniqueness of line graphs (submitted)
19. Noy, M.: Graphs determined by polynomial invariants. Theor. Comput. Sci. 307, 365-384 (2003)
20. Oxley, J.G.: Matroid Theory. Oxford: Oxford University Press 1992
21. Read, R.C., Tutte, W.T.: Chromatic polynomials. In: L.W. Beineke and R.J. Wilson: Selected Topics in Graph Theory 3, pp. 15-42, London: Academic Press 1988
22. Sarmiento, I.: A characterisation of jointless Dowling geometries. Discrete Math. 197/198, 713-731 (1999)
23. Tutte, W.T.: Codichromatic Graphs. J. Comb. Theory, Ser. B 16, 168-174 (1974)
24. Welsh, D.J.A.: Complexity: knots, colourings and counting. Cambridge: Cambridge University Press 1993