The Hamiltonian property of generalized de Bruijn digraphs

The Hamiltonian property of generalized de Bruijn digraphs

Rainbow Domination in Generalized de Bruijn Digraphs

In this paper, we are concerned with the krainbow domination problem on generalized de Bruijn digraphs. We give an upper bound and a lower bound for the k-rainbow domination number in generalized de Bruijn digraphs GB(n, d). We also show that γrk(GB(n, d)) = k if and only if α 6 1, where n = d+α and γrk(GB(n, d)) is the k-rainbow domination number of GB(n, d).

On the Domination Numbers of Generalized de Bruijn Digraphs and Generalized Kautz Digraphs

This work deals with the domination numbers of generalized de Bruijn digraphs and generalized Kautz digraphs. Dominating sets for digraphs are not familiar compared with dominating sets for undirected graphs. Whereas dominating sets for digraphs have more applications than those for undirected graphs. We construct dominating sets of generalized de Bruijn digraphs where obtained dominating sets ...

Restricted Edge-Connectivity of de Bruijn Digraphs

The restricted edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks. This paper determines that the restricted edge-connectivity of the de Bruijn digraph B(d, n) is equal to 2d − 2 for d ≥ 2 and n ≥ 2 except B(2, 2). As consequences, the super edge-connectedness of B(d, n) is obtained immediately.

Feedback numbers of de Bruijn digraphs

A subset of vertices of a graph G is called a feedback vertex set of G if its removal results in an acyclic subgraph. Let f (d, n) denote the minimum cardinality over all feedback vertex sets of the de Bruijn digraph B(d, n). This paper proves that for any integers d ≥ 2 and n ≥ 2 f (d, n) =  1 n ∑ i|n diφ (n i ) for 2 ≤ n ≤ 4; dn n + O(ndn−4) for n ≥ 5, where i | nmeans i divides n, and ...