Strongly cospectral vertices in normal Cayley graphs

Abstract

We prove an upper bound on the number of pairwise strongly cospectral vertices in a normal Cayley graph, in terms of the multiplicities of its eigenvalues. We use this to determine an explicit bound in Cayley graphs of ${\mathbb{Z}}_2^d$ and ${\mathbb{Z}}_4^d$. We also provide some infinite families of Cayley graphs of ${\mathbb{Z}}_2^d$ with a set of four pairwise strongly cospectral vertices and show that such graphs exist in every dimension.

23 pages, 4 figures

References in corpus (4)

• Perfect Transfer of Arbitrary States in Quantum Spin Networks
• Quantum Networks on Cubelike Graphs
• Strongly Cospectral Vertices
• Continuous-time Quantum Walks on Cayley Graphs of Extraspecial Groups

Cited by in corpus (2)

• Strong Cospectrality and Twin Vertices in Weighted Graphs
• Constructing Cospectral Vertices Through Orbits of Subgraphs