Partial Domination in Prisms of Graphs

2022/01/10 by L. Philo Nithya, Nithya, L. Philo, Joseph Varghese Kureethara +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2201.03563

openalex publication_date 2022/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any graph G = (V, E) and proportion p∈(0,1], a set S⊆ V is a p-dominating set if (|N[S]|)/(|V|)≥ p. The p-domination number γ_p(G) equals the minimum cardinality of a p-dominating set in G. For a permutation π of the vertex set of G, the graph πG is obtained from two disjoint copies G₁ and G₂ of G by joining each v in G₁ to π(v) in G₂. i.e., V(π G)= V(G₁)∪ V(G₂) and E(G)= E(G₁)∪ E(G₂)∪ \\v,π(v)\: v∈ V(G₁), π(v)∈ V(G₂)\. The graph π G is called the prism of G with respect to π. In this paper, we find some relations between the domination and the p-domination numbers in the context of graph and its prism graph for particular values of p.

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• Properties of Partial Dominating Sets of Graphs
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