منابع مشابه
Dihedral Groups Ii
1. Abstract characterization of Dn The group Dn has two generators r and s with orders n and 2 such that srs−1 = r−1. We will show any group with a pair of generators like r and s (except for their order) admits a homomorphism onto it from Dn, and is isomorphic to Dn if it has the same size as Dn. Theorem 1.1. Let G be generated by elements a and b where an = 1 for some n ≥ 3, b2 = 1, and bab−1...
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We examine two particular constructions that derive from a 2-group G = G(·) another 2-group G(∗) for the case when G(·) is one of D2n , SD2n , Q2n . The constructions (the cyclic one and the dihedral one) have the property that x ∗ y = x · y for exactly 3/4 of all pairs (x, y) ∈ G × G. If G(◦) and G(∗) are such 2-groups that x ◦ y 6= x ∗ y for less then a quarter of all pairs (x, y) ∈ G × G, th...
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A k-L(2, 1)-labelling of a graph G is a mapping f : V (G) → {0, 1, 2, . . . , k} such that |f(u)− f(v)| ≥ 2 if uv ∈ E(G) and f(u) 6= f(v) if u, v are distance two apart. The smallest positive integer k such that G admits a k-L(2, 1)-labelling is called the λ-number of G. In this paper we study this quantity for cubic Cayley graphs (other than the prism graphs) on dihedral groups, which are call...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2005
ISSN: 0030-8730
DOI: 10.2140/pjm.2005.222.301