Coboundary Polynomial

The coboundary polynomial chi^__G(q,t) is a bivariate graph polynomial which can be expressed in terms of the Tutte polynomial T_G(x,y) of a graph G by


where c_G is the connected component count and n_G is the vertex count of a graph G (Martin and Reiner 2005; Ardila 2007).

The coboundary polynomial provides a particularly concise way of expression generating functions for the Tutte polynomial of a complete graph K_n or complete bipartite graph K_(m,n).

See also

Graph Rank, Tutte Polynomial

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Ardila, F. "Computing the Tutte Polynomial of a Hyperplane Arrangement." Pacific J. Math. 230, 1-26, 2007.Martin, J. and Reiner, V. "Cyclotomic and Simplicial Matroids." Israel J. Math. 150, 229-240, 2005.

Cite this as:

Weisstein, Eric W. "Coboundary Polynomial." From MathWorld--A Wolfram Web Resource.

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