Dec 31, 2022 · Given a graph G = ( V , E ) , a set S ⊆ V is said to be a dominating set if every vertex in V ∖ S is adjacent to some vertex in S .

Oct 22, 2024 · Given a graph G, a set Dk⊆V(G) is said to be k-dominating if every vertex in V(G)∖Dk has at least k neighbors in Dk. The k-domination number ...

Dec 31, 2022 · Given a graph G, a set D k ⊆ V ( G ) is said to be k-dominating if every vertex in V ( G ) ∖ D k has at least k neighbors in D k.

Given a graph G, a set Dk⊆V(G) is said to be k-dominating if every vertex in V(G)∖Dk has at least k neighbors in Dk. The k-domination number γk(G) is the ...

This paper introduces the concept of proper 2-dominating sets in graphs, providing a comprehensive characterisation of graphs that possess such sets.

Jun 30, 2023 · γt(G) represents the minimum size of a total dominating set of G.γ(G) represents the minimum size of a dominating set in G. Obviously we have γt ...

Dec 23, 2017 · Minimum degree of the graph is a local property. With knowing the minimum degree of a graph, we don't have any information about other vertices ...

This article investigates upper bounds on the k-domination number for d-regular graphs with a fixed d ≥ 3, and demonstrates that the same bounds are applicable ...

Dec 5, 2023 · We prove that Min-DD2 and Max-DD2 are approximable within a factor of 3. 2. For any 3-regular graph, we show that the Min-DD2 and Max-DD2 are ...