On the reconstruction of graph invariants

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 ξ and the colored versions of the latter two are reconstructible. We also present a method of reconstructing boolean graph invariants, or in other words, proving recognizability of (possibly colored) graph properties, using first order logic.