A dominating function f of G is said to be minimal dominating function if whenever g<f, g is not a dominating function of G. Let G = (V,E) be a graph without isolated vertices. A subset T of V is called a total dominating set of G if every vertex in V is adjacent to at least one vertex in T.
Mar 4, 2010 · A dominating function for a graph is a function from its vertex set into the unit interval so that the sum of function values taken over the ...
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A set S of vertices in G is a dominating set of G if every vertex of G is dominated by at least one vertex in S. The minimum number of vertices in a dominating ...
Mar 23, 2024 · If G is a graph with no isolated vertex, then there exists a minimum dominating set S in G with the property that every vertex of S has an S-external private ...
The dominating function f is called a minimal dominating function (MDF),if f doesn 't remain a DF when the function value at some vertex is reduced.In this ...
In this paper, we establish upper bounds on this maximum number of minimal dominating sets for split graphs, cobipartite graphs and interval graphs.
Apr 23, 2023 · I am searching for a graph that satisfies the property of all minimal dominating sets avoiding a specific vertex.
In this paper we study some of the structural properties of the set of all minimal total dominating functions (#T ) of cycles and paths and.
Chain graphs. In this section, we combine a study of structural properties of minimal dominating sets in chain graphs with combinatorial arguments to exactly ...
Feb 14, 2024 · We develop non-trivial enumeration algorithms for minimal Roman dominating functions with polynomial delay and polynomial space.