Strong domination number of a modified graph

2022/12/04 by ‎Saeid Alikhani, Alikhani, Saeid, Nima Ghanbari +1
Computer Science · Neuroscience · #05C15 #05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Nuclear Receptors and Signaling

paper · pdf · doi:10.48550/arxiv.2212.01860

openalex publication_date 2022/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G=(V,E) be a simple graph. A set D⊆ V is a strong dominating set of G, if for every vertex x∈ V∖ D there is a vertex y∈ D with xy∈ E(G) and deg(x)≤ deg(y). The strong domination number γ_st(G) is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on γ_st(G) when G is modified by operations on vertex and edge of G.

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