The fractional analogues of domination and packing in a graph form an interesting pair of dual linear programs in that the feasible vectors for both LPs have interpretations as functions from the vertices of the graph to the unit interval; efficient (fractional) domination is accomplished when a function simultaneously solves both LPs. We investigate some structural properties of the functions ...

Optimality Theory (OT) and Harmonic Grammar (HG) differ because the former assumes a model of constraint interaction based on strict domination, while the latter assumes a weighted model of interaction. As Prince and Smolensky (1997) admit, “that strict domination governs grammatical constraint interaction is not currently explained”. Yet, Legendre et al. (2006, 911-912) make two suggestions. T...

In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). We show that subk(G) is a computationally efficient sharp lower bound on the k-domination number of G, and improves on several known lower bounds. We also characterize the sub-k-domination numbers of several families of graphs, provide...

A graph is an efficient open domination graph if there exists a subset of vertices whose open neighborhoods partition its vertex set. We characterize those graphs G for which the Cartesian product G H is an efficient open domination graph when H is a complete graph of order at least 3 or a complete bipartite graph. The characterization is based on the existence of a certain type of weak partiti...

We generalize the concept of efficient total domination from graphs to digraphs. An efficiently total dominating set X of a digraph D is a vertex subset such that every vertex of D has exactly one predecessor in X . We study graphs that permit an orientation having such a set and give complexity results and characterizations concerning this question. Furthermore, we study the computational comp...

Let G be a digraph. A set S ⊆ V (G) is called an efficient total dominating set if the set of open out-neighborhoods N−(v) ∈ S is a partition of V (G). We say that G is efficiently open-dominated if both G and its reverse digraph G− have an efficient total dominating set. Some properties of efficiently open dominated digraphs are presented. Special attention is given to tournaments and directed...

An efficiently total dominating set of a graph G is a subset of its vertices such that each vertex of G is adjacent to exactly one vertex of the subset. If there is such a subset, then G is an efficiently total dominable graph (G is etd). In this paper, we prove NP-completeness of the etd decision problem on the class of planar bipartite graphs of maximum degree 3. Furthermore, we give an effic...

Let Heff (Veff, Eeff) be a finite simple connected graph of order m with vertex set Veff and edge Eeff. A dominating Sds⊆Veff is called an efficiently if, for every ua∈VG, NGua∩Sds=1—where NG [ua] denotes the closed neighborhood ua. Using efficient domination techniques labelling, we constructed fuzzy network. An algorithm has been framed to encrypt decrypt secret information present in network...