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Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
Non-Isomorphic Optimal Cayley Graphs
Francesc Comellas · 2026-06-09 · via math.CO updates on arXiv.org

We present more than seventy 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.