Results about wreath products of circulant graphs are used to construct infinitely many circulant graphswith efficient dominating setswhose elements need not be equally spaced in Zn. It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulant graph with an efficient...

Let G = (V; E) be a /nite and undirected graph without loops and multiple edges. An edge is said to dominate itself and any edge adjacent to it. A subset D of E is called a perfect edge dominating set if every edge of E \ D is dominated by exactly one edge in D and an e cient edge dominating set if every edge of E is dominated by exactly one edge in D. The perfect (e cient) edge domination prob...

The bondage number of a graph G is the minimum number of edges whose removal results in a graph with larger domination number.A dominating setD is called an efficient dominating set ofG if |N−[v]∩D|=1 for every vertex v ∈ V (G). In this paper we establish a tight lower bound for the bondage number of a vertex-transitive graph. We also obtain upper bounds for regular graphs by investigating the ...

Vizing’s conjecture on the Cartesian product G H of two graphs, γ(G H) ≥ γ(G)γ(H), will hold for all graphs G if the domination and (closed neighborhood) packing number of G are equal. By using the theory of integer programming, we state known sufficient conditions for when the packing number and the domination number of a graph are equal. We also give a sufficient condition using the theory of...

Let D be a digraph. Its reverse digraph, D−1, is obtained by reversing all arcs of D. We show that the domination numbers of D and D−1 can be different if D is a Cayley digraph. The smallest groups admitting Cayley digraphs with this property are the alternating group A4 and the dihedral group D6, both on 12 elements. Then, for each n ≥ 6 we find a Cayley digraph D on the dihedral group Dn such...

In this paper, we tackle the problem of efficient skycube computation. We introduce a novel approach significantly reducing domination tests for a given subspace and the number of subspaces searched. Technically, we identify two types of skyline points that can be directly derived without using any domination tests. Moreover, based on formal concept analysis, we introduce two closure operators ...