Elimination properties for minimal dominating sets of graphs

minimal, vertex minimal and commonality minimal cn-dominating graphs

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

Enumerating Minimal Connected Dominating Sets in Graphs of Bounded Chordality

Listing, generating or enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality. We establish enumeration algorithms as well as lower and upper bound...

On maximum number of minimal dominating sets in graphs

Strength of strongest dominating sets in fuzzy graphs

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...

Minimal dominating sets in interval graphs and trees

We show that interval graphs on n vertices have at most 3 ≈ 1.4422 minimal dominating sets, and that these can be enumerated in time O∗(3n/3). As there are examples of interval graphs that actually have 3 minimal dominating sets, our bound is tight. We show that the same upper bound holds also for trees, i.e. trees on n vertices have at most 3 ≈ 1.4422 minimal dominating sets. The previous best...