Abstract. A dominating set S of a graph G is called efficient if |N[v]∩S| = 1 for every vertex v ∈ V (G). That is, a dominating set S is efficient.
Jul 20, 2021 · Such a function is efficient if all of the vertex inequalities are met with equality. They give a simple necessary condition for efficient ...
PDF | A dominating set S of a graph G is called efficient if |N [v] ∩ S| = 1 for every vertex v ∈ V (G). That is, a dominating set S is efficient if and.
In this paper, we investigate efficient multiple domination. There are several types of multiple domination defined in the literature: k-tuple domination, {k}- ...
Efficient (j, k)-Dominating Functions - UNF Digital Commons
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Jan 1, 2020 · The problem of deciding whether a given graph has an efficient (j, k)-dominating function is shown to be NP-complete for all positive integers j ...
Duration: 55:03
Posted: Nov 12, 2020
Posted: Nov 12, 2020
This paper investigates efficient versions of the first two types of k-tuple domination as well as a new type of multiple domination called k-domination ...
Oct 22, 2024 · A set of vertices S of a graph G is convex if all vertices of every geodesic between two of its vertices are in S. We say that G is k-convex if ...
Conditions for Efficient (j, k)-Domination. Henry Fleischmann∗ (University ... We characterize efficient (j, k)-dominating functions on strong products of graphs ...
The main result of Section 4 is that, for all integers j and k, it is NP-complete to decide whether a given graph has an efficient (j, k)- dominating function.