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A Frobenius group is a transitive permutation group which is not regular but only the identity element can fix two points. Such a group can be expressed as the semidirect product G=K⋊H of a nilpotent normal subgroup K and another group H fixing a point. A first-kind G-Frobenius graph is a connected Cayley graph on K with connection set an H-orbit aH on K that generates K, where H has an even order...
Given integers n ≥ 7 and a, b, c with 1 ≤ a, b, c ≤ n − 1 such that a, n − a, b, n − b, c, n − c are pairwise distinct, the (undirected) triple‐loop network TLn(a, b, c) is the degree‐six graph with vertices 0, 1, 2,…,n − 1 such that each vertex x is adjacent to x ± a, x ± b, and x ± c, where the operation is modulo n. It is known that the maximum order of a connected triple‐loop network of the form...
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