A w-container C(u,v) of a graph G is a set of w-disjoint paths joining u to v. A w-container of G is a w*-container if it contains all the nodes of V(G). A bipartite graph G is w*-laceable if there exists a w*-container between any two nodes from different parts of G. Let n and k be any two positive integers with n ) 1 and k ( n+1. In this paper, we prove that n-dimensional bipartite hypercube-like graphs are f-edge fault kâ-laceable for every f ( n-1 and f+k ( n+1.
COBISS.SI-ID: 1024516436
A vertex-transitive graph X is said to be half-arc-transitive if its automorphism group acts transitively on the set of edges of X but does not act transitively on the set of arcs of X. A classification of half-arc-transitive graphs on 4p vertices, where p is a prime, is given. Apart from an obvious infinite family of metacirculants, which exist for p=1(mod 4) and have been known before, there is an additional somewhat unique family of half-arc-transitive graphs of order 4p and valency 12; the latter exists only when p=1(mod 6) is of the form 2^{2k}+2^k+1, k ) 1.
COBISS.SI-ID: 4182632
A graph X is said to be G-arc-regular if a subgroup G (= Aut(X) acts regularly on the arcs of X. In this paper connected G-arc-regular graphs are classified in the case when G contains a regular dihedral subgroup D_{2n} of order 2n whose cyclic subgroup C_n (= D_{2n} of index 2 is core-free in G. As an application, all regular Cayley maps over dihedral groups D_{2n}, n odd, are classified.
COBISS.SI-ID: 1024473940