Cycle decompositions IV: complete directed graphs and fixed length directed cycles

On independent domination numbers of grid and toroidal grid directed graphs

A subset $S$ of vertex set $V(D)$ is an {em indpendent dominating set} of $D$ if $S$ is both an independent and a dominating set of $D$. The {em indpendent domination number}, $i(D)$ is the cardinality of the smallest independent dominating set of $D$. In this paper we calculate the independent domination number of the { em cartesian product} of two {em directed paths} $P_m$ and $P_n$ for arbi...

Cycle Decompositions Iii: Complete Graphs and Fixed Length Cycles

Independent domination in directed graphs

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...

Directed 3-cycle decompositions of complete directed graphs with quadratic leaves

Let G be a vertex-disjoint union of directed cycles in the complete directed graph Dt , let |E(G)| be the number of directed edges of G and suppose G 6= ⇀ C 2 ∪ ⇀ C 3 or ⇀ C 5 if t = 5, and G 6= ⇀ C 3 ∪ ⇀ C 3 if t = 6. It is proved in this paper that for each positive integer t , there exist ⇀ C 3-decompositions for Dt − G if and only if t(t − 1)− |E(G)| ≡ 0 (mod 3). © 2008 Elsevier B.V. All ri...

The Dynamics of Directed NOR Networks

This work investigates the dynamics of simultaneously updated boolean networks defined on directed graphs, where each vertex updates to the logical NOR value of the states of the vertices in its in-neighborhood. We prove the existence and number of limit cycles and the width of state space graphs for directed cycles, complete graphs, and complete bipartite graphs. We show that every strongly co...