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arXiv · 2606.10954

Non-Isomorphic Optimal Cayley Graphs

Francesc Comellas
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Abstract

We present eighty-nine optimal degree-diameter Cayley graphs that are non-isomorphic to previously known optimal Cayley graphs with the same degree and diameter. For each graph, we provide comprehensive data on its parameters and structural invariants. Comparison with known constructions reported by Marston Conder on the Combinatorics Wiki and in related works reveals significant differences in girth, algebraic connectivity, domination number, automorphism group structure, cycle distributions, distance-related properties, and other graph invariants. These findings show that optimal degree-diameter Cayley graphs are frequently non-unique. The new examples enlarge the catalogue of known optimal graphs and provide benchmarks for investigations in degree-diameter problems, algebraic graph theory, and extremal graph theory. Since some of the graphs were identified through randomized search techniques, the collection is not exhaustive.

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Francesc Comellas. 2026-06-23. Non-Isomorphic Optimal Cayley Graphs. https://arxiv.org/abs/2606.10954

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