Security in Sierpiński graphs

Menon, Manju K.; M.R., Chithra; K.S., Savitha

doi:10.1016/j.dam.2022.11.017

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 2011, Gravier, Kovše, and Parreau [7] introduced a generalization in such a way that any graph can act as a fundamental graph, and called the resulting graphs generalized Sierpiński graphs. We refer to the papers [1,4,5,13,14,16,17,20,21,22,24] for investigations of generalized Sierpiński graphs in the last few years.…”

Section: Introductionmentioning

confidence: 99%

The Sierpiński domination number

Henning,

Klavžar,

Kleszcz

et al. 2024

Ars Math. Contemp.

View full text Add to dashboard Cite

Let G and H be graphs and let f : V (G) → V (H) be a function. The Sierpiński product of G and H with respect to f , denoted by G ⊗ f H, is defined as the graph on the vertex set V (G) × V (H), consisting of |V (G)| copies of H; for every edge gg ′ of G there is an edge between copies gH and g ′ H of H associated with the vertices g and g ′ of G, respectively, of the form (g, f (g ′ ))(g ′ , f (g)). In this paper, we define the Sierpiński domination number as the minimum of γ(G ⊗ f H) over all functions f : V (G) → V (H). The upper Sierpiński domination number is defined analogously as the corresponding maximum.* We would like to thank the reviewer very much for careful reading of the paper and in particular for pointing to a subtle technical detail that led to the reformulation of one of the main theorems.

show abstract