Strong domination number of some operations on a graph

2022/10/20 by ‎Saeid Alikhani, Alikhani, Saeid, Nima Ghanbari +3
Computer Science · #05C15 #05C25 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2210.11120

openalex publication_date 2022/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G=(V(G),E(G)) be a simple graph. A set D⊆ V(G) is a strong dominating set of 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) is defined as the minimum cardinality of a strong dominating set. In this paper, we examine the effects on γ_st(G) when G is modified by operations on edge (or edges) of G.

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