A combinatorial approach to the algebra of hypermatrices

TL;DR

This paper introduces two hypermatrix formulations of the Cayley Hamilton theorem, extending classical combinatorial interpretations and applying the results to graph invariants for distinguishing non-isomorphic graphs.

Contribution

It presents novel hypermatrix formulations of the Cayley Hamilton theorem that extend combinatorial interpretations and demonstrate applications in graph theory.

Findings

Two hypermatrix formulations of the Cayley Hamilton theorem

Extension of combinatorial interpretations to hypermatrices

Application to graph invariants for non-isomorphic graphs

Abstract

We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing an application of the theorem to computing graph invariants which distinguish some non-isomorphic graphs with isospectral adjacency matrices.