Linear Recurrence Relations for Graph Polynomials

A sequence of graphs Gn is iteratively constructible if it can be built from an initial labeled graph by means of a repeated fixed succession of elementary operations involving addition of vertices and edges, deletion of edges, and relabelings. Let Gn be a iteratively constructible sequence of graphs. In a recent paper, [27], M. Noy and A. Rib`o have proven linear recurrences with polynomial coefficients for the Tutte polynomials T(Gi, x, y) = T(Gi), i.e. T(Gn+r) = p1(x, y)T(Gn+r-1) + . . . + pr(x, y)T(Gn). We show that such linear recurrences hold much more generally for a wide class of graph polynomials (also of labeled or signed graphs), namely they hold for all the extended MSOL-definable graph polynomials. These include most graph and knot polynomials studied in the literature.

• Type: Conference
• Year: 2008
• Where: BIRTHDAY
• Authors: Eldar Fischer, Johann A. Makowsky
• Keywords: Applied Computing, BIRTHDAY 2008, Graph Polynomials, Initial Labeled Graph, Linear Recurrences