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سند علمی

Infinitely many one-regular Cayley graphs on dihedral groups of any prescribed valency

Jin Ho Kwak, Young Soo Kwon, Ju-Mok Oh

چکیده

A graph is one-regular if its automorphism group acts regularly on the arc set. In this paper, we construct a new infinite family of one-regular Cayley graphs of any prescribed valency. In fact, for any two positive integers , k 2 except for ( , k) ∈ {(2,3), (2,4)}, the Cayley graph Cay(Dn,S) on dihedral groups Dn = 〈a, b | an = b2 = (ab)2 = 1〉 with S = {a1+ +···+ t b | 0 t k − 1} and n = ∑k−1 j=0 j is oneregular. All of these graphs have cyclic vertex stabilizers and girth 6. As a continuation of Marušič and Pisanski’s classification of cubic one-regular Cayley graphs on dihedral groups in [D. Marušič, T. Pisanski, Symmetries of hexagonal graphs on the torus, Croat. Chemica Acta 73 (2000) 969–981], the 5-valent oneregular Cayley graphs on dihedral groups are classified. Also, with only finitely many possible exceptions, all of one-regular Cayley graphs on dihedral groups of any prescribed prime valency are constructed. © 2007 Elsevier Inc. All rights reserved.

اسناد مشابه

  • Infinitely many one-regular Cayley graphs on dihedral groups of any prescribed valency

    مقاله‌ی دسترسی آزاد۲۰۰۸Journal of Combinatorial Theory, Series BJin HoKwak, Young SooKwon, Ju-MokOh

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    Let Γ = Cay(G, S) and G ≤ X ≤ AutΓ. We say Γ is (X, 1)-regular Cayley graph if X acts regularly on its arcs. Γ is said to be corefree if G is core-free in some X ≤ Aut(Cay(G, S)). In this paper, we prove that if an (X, 1)-regular Cayley graph of valency 5 is not normal or binorma

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    In this paper, we construct some directed strongly regular Cayley graphs on Dihedral groups, which generalizes earlier constructions. We also characterize certain groups Dpα, where p is a prime and α ≥ 1 positive integer.

  • Strongly regular Cayley graphs over primary abelian groups of rank 2

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