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.
From: Hiranmoy Pal [view email]
[v1]
Mon, 12 May 2025 18:26:59 UTC (7 KB)
[v2]
Fri, 20 Jun 2025 06:25:20 UTC (17 KB)
[v3]
Fri, 26 Dec 2025 06:56:01 UTC (18 KB)
[v4]
Sun, 2 Aug 2026 04:06:28 UTC (23 KB)
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