Strong domination number of graphs from primary subgraphs

2023/06/02 by ‎Saeid Alikhani, Alikhani, Saeid, Nima Ghanbari +3 · 1 citation
Computer Science · Neuroscience · #Advanced Graph Theory Research #Nuclear Receptors and Signaling #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2306.01608

Abstract

A set D of vertices is a strong dominating set in a graph G, if for every vertex x∈ V(G) ∖ D there is a vertex y∈ D with xy∈ E(G) and deg(x) ≤ deg(y). The strong domination number γ_st(G) of G is the minimum cardinality of a strong dominating set in G. Let G be a connected graph constructed from pairwise disjoint connected graphs G₁,… ,G_k by selecting a vertex of G₁, a vertex of G₂, and identifying these two vertices, and thereafter continuing in this manner inductively. The graphs G₁,… ,G_k are the primary subgraphs of G. In this paper, we study the strong domination number of K_r-gluing of two graphs and investigate the strong domination number for some particular cases of graphs from their primary subgraphs.

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