On the Reconstruction of Graph Invariants

Details On the Reconstruction of Graph Invariants On the Reconstruction of Graph Invariants

2009-05-12

arxiv.org/abs/0905.1915v4

Mathematics

Combinatorics

Scientific paper

The reconstruction conjecture has remained open for simple undirected graphs since it was suggested in 1941 by Kelly and Ulam. In an attempt to prove the conjecture, many graph invariants have been shown to be reconstructible from the vertex-deleted deck, and in particular, some prominent graph polynomials. Among these are the Tutte polynomial, the chromatic polynomial and the characteristic polynomial. We show that the interlace polynomial, the U -polynomial, the universal edge elimination polynomial xi and the colored versions of the latter two are reconstructible.

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