On generalized Sierpi\'nski graphs

Rodríguez-Velázquez, Juan A.; Rodríguez-Bazan, Erick D.; Estrada‐Moreno, Alejandro

doi:10.7151/dmgt.1945

Cited by 6 publications

(3 citation statements)

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“…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.

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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.

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Section: Introductionmentioning

confidence: 99%

The Sierpiński domination number

Henning,

Klavžar,

Kleszcz

et al. 2024

Ars Math. Contemp.

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“…Hinz and Parisse studied the eccentricity of an arbitrary vertex of Sierpi ński graphs in [31] where the main result gave an expression for the average eccentricity of S(K n , t). Rodríguez-Velázquez et al obtained closed formulae for several parameters of generalized Sierpi ński graphs S(G, t) in terms of parameters of the base graph G; especially, they studied the chromatic, vertex cover, clique, and domination numbers [32]. Ishfaq et al computed the Zagreb and forgotten invariants for extended Sierpi ński graphs.…”

Section: Introductionmentioning

confidence: 99%

On Entropy of Some Fractal Structures

et al. 2023

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Shannon entropy, also known as information entropy or entropy, measures the uncertainty or randomness of probability distribution. Entropy is measured in bits, quantifying the average amount of information required to identify an event from the distribution. Shannon’s entropy theory initiates graph entropies and develops information-theoretic magnitudes for structural computational evidence of organic graphs and complex networks. Graph entropy measurements are valuable in several scientific fields, such as computing, chemistry, biology, and discrete mathematics. In this study, we investigate the entropy of fractal-type networks by considering cycle, complete, and star networks as base graphs using degree-based topological indices.

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“…Later, the total chromatic number of generalized Sierpiński graphs was studied in [7] and the strong metric dimension has recently been studied in [5]. The authors of [33] obtained closed formulae for the chromatic, vertex cover, clique and domination numbers of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. More recently, a general upper bound on the Roman domination number of S(G, t) was obtained in [28]. In particular, it was studied the case in which the base graph G is a path, a cycle, a complete graph or a graph having exactly one universal vertex.…”

Section: Introductionmentioning

confidence: 99%

On the General Randić index of polymeric networks modelled by generalized Sierpiński graphs

Estrada‐Moreno

Rodríguez-Velázquez

2019

Discrete Applied Mathematics

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The General Randić index R α of a simple graph G is defined aswhere d(v i ) denotes the degree of the vertex v i . Rodríguez-Velázquez and Tomás-Andreu [MATCH Commun. Math. Comput. Chem. 74 (1) (2015) 145-160] obtained closed formulae for the Randić index R −1/2 of Sierpiński-type polymeric networks, where the base graph is a complete graph, a triangle-free regular graph or a bipartite semiregular graph. In the present article we obtain closed formulae for the general Randić index R α of Sierpiński-type polymeric networks, where the base graph is arbitrary.

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On generalized Sierpi\'nski graphs

Abstract: In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.

Cited by 6 publications

References 6 publications

The Sierpiński domination number

The Sierpiński domination number

On Entropy of Some Fractal Structures

On the General Randić index of polymeric networks modelled by generalized Sierpiński graphs

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