We investigate the existence of Hamilton paths in connected Cayley graphs on generalized dihedral groups. In particular, we show that a connected Cayley graph of valency at least three on a generalized dihedral group, whose order is divisible by four, is Hamiltonconnected, unless it is bipartite, in which case it is Hamilton-laceable.
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 gr
The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of
In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G = Cay(D2n, Ω) constructed on the finite dihedral group D2n, and a specified generating set Ω of D2n. Further efficient dominating sets in G
A Cayley graph Γ = Cay(G, S) is called normal for G, if GR, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ ) of Γ . In this paper we determine the normality of connected and undirected Cayley graphs of valency three for dihedral g
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
Slovenija Abstract A partial extension of the results in 1], where 2-arc-transitive cir-culants are classiied, is given. It is proved that a 2-arc-transitive Cayley graph of a dihedral group is either a complete graph or a bi-partite graph.