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arXiv · 2505.07982

More graphs with pair state transfer

Hermie Monterde·Hiranmoy Pal
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Abstract

This paper has two main goals. First, we characterize perfect state transfer between $s$-pair states in strongly regular graphs, as well as graphs in association schemes admitting perfect state transfer between vertices. The second goal is to provide a unified approach for constructing non-regular graphs admitting pair state transfer$-$relative to the adjacency, Laplacian, and signless Laplacian matrix$-$between the same pair of states at the same time. In particular, we show that for each $k\geq 5$, there are infinitely many connected graphs with maximum valency $k$ admitting this property. We also utilize graph products to generate new infinite families of graphs with pair state transfer.

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Hermie Monterde, Hiranmoy Pal. 2025-05-12. More graphs with pair state transfer. https://arxiv.org/abs/2505.07982

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