The incidence Hopf algebra of graphs

Details The incidence Hopf algebra of graphs The incidence Hopf algebra of graphs

2010-12-21

arxiv.org/abs/1012.4786v3

Mathematics

Combinatorics

17 pages; final version to appear in SIAM J. Discrete Math

Scientific paper

The graph algebra is a commutative, cocommutative, graded, connected incidence Hopf algebra, whose basis elements correspond to finite simple graphs and whose Hopf product and coproduct admit simple combinatorial descriptions. We give a new formula for the antipode in the graph algebra in terms of acyclic orientations; our formula contains many fewer terms than Takeuchi's and Schmitt's more general formulas for the antipode in an incidence Hopf algebra. Applications include several formulas (some old and some new) for evaluations of the Tutte polynomial.

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