Graphs determined by polynomial invariants

Authors:
Marc Noy
Affiliations:
Department de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, 5 Pau Gargallo, Barcelona 08028, Spain
Venue:
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Year:
2003

Citing 14
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Abstract

Many polynomials have been defined associated to graphs, like the characteristic, matchings, chromatic and Tutte polynomials. Besides their intrinsic interest, they encode useful combinatorial information about the given graph. It is natural then to ask to what extent any of these polynomials determines a graph and, in particular, whether one can find graphs that can be uniquely determined by a given polynomial. In this paper we survey known results in this area and, at the same time, we present some new results.