Graph parameters from symplectic group invariants

Guus Regts, Bart Sevenster

Published 2016-02-05Version 1

In this paper we introduce, and characterize, a class of graph parameters obtained from tensor invariants of the symplectic group. These parameters are similar to partition functions of vertex models, as introduced by de la Harpe and Jones, [P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical mechanical models: examples and problems, {\sl Journal of Combinatorial Theory}, Series B {\bf 57} (1993) 207--227]. Yet they give a completely different class of graph invariants. We moreover show that certain evaluations of the cycle partition polynomial give examples of graph parameters that can be obtained this way.