## Algebraic combinatorics in mathematical chemistry. Methods and algorithms. I: Permutation groups and coherent (cellular) algebras.(English)Zbl 1029.05151

Summary: Let $$(G,\Omega)$$ be a permutation group of degree $$n$$. Let $$V(G,\Omega)$$ be the set of all square matrices of order $$n$$ which commute with all permutation matrices corresponding to permutations from $$(G,\Omega)$$. $$V(G,\Omega)$$ is a matrix algebra which is called the centralizer algebra of $$(G,\Omega)$$. In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the properties of these algebras. It turns out that coherent algebras provide a very helpful tool for the investigation of the symmetries of graphs of different kinds, in particular, of molecular graphs.

### MSC:

 05C90 Applications of graph theory 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

nauty