2011•arXiv (Cornell University)Open access

Cellular Algebras and Graph Invariants Based on Quantum Walks

Jamie Smith

Abstract

We consider two graph invariants inspired by quantum walks- one in continuous time and one in discrete time. We will associate a matrix algebra called a cellular algebra with every graph. We show that, if the cellular algebras of two graphs have a similar structure, then they are not distinguished by either of the proposed invariants.

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Key concepts: Graph, Quantum walk, Mathematics, Quantum, Graph algebra, Algebra over a field, Discrete mathematics, Pure mathematics