Sierpiński graphs as spanning subgraphs of Hanoi graphs

Hinz, Andreas M.; Klavžar, Sandi; Zemljič, Sara Sabrina

doi:10.2478/s11533-013-0227-7

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…Sierpiński graphs have been extensively studied in most graph-theoretical aspects as well as in other areas of mathematics and even psychology. Some notable papers are [11,13,15,17,18,22,26,27]. An extensive summary of topics studied on and around Sierpiński graphs is available in the survey paper by Hinz, Klavžar and Zemljič [12].…”

Section: Introductionmentioning

confidence: 99%

The Sierpiński product of graphs

et al. 2022

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Section: Introductionmentioning

confidence: 99%

The Sierpiński product of graphs

et al. 2022

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“…Sierpiński graphs were first introduced in 1997 by Klavžar and Milutinović [8] stemming from their work on the Tower of Hanoi problem. Since then, numerous properties and generalizations of Sierpiński graphs have been extensively studied (e.g., see [6,7,9,10,12,13], and [14]). Recently, Kovič, Pisanski, Zemljič, andŽitnik [11] have used Sierpiński graphs as a motivation for a graph product structure, which they referred to as a Sierpiński product.…”

Section: Introductionmentioning

confidence: 99%

Sierpiński products of r-uniform hypergraphs

Budden

Hiller

2022

Art Discrete Appl. Math.

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If H 1 and H 2 are r-uniform hypergraphs and f is a function from the set of all (r − 1)element subsets of V (H 1 ) into V (H 2 ), then the Sierpiński product H 1 ⊗ f H 2 is defined to have vertex set V (H 1 ) × V (H 2 ) and hyperedges falling into two classes:. We develop the basic structure possessed by this product and offer proofs of numerous extremal properties involving connectivity, clique numbers, and strong chromatic numbers.

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“…Sierpiński graphs have been extensively studied in most graph-theoretical aspects as well as in other areas of mathematics and even psychology. Some notable papers are [8,10,12,14,16,19,23,24]. An extensive summary of topics studied on and around Sierpiński graphs is available in the survey paper by Hinz, Klavžar and Zemljič [9].…”

Section: Introductionmentioning

confidence: 99%

The Sierpiński product of graphs

Kovič¹,

Pisanski²,

Zemljič³

et al. 2019

Preprint

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In this paper we introduce a product-like operation that generalizes the construction of generalized Sierpiński graphs. Let G, H be graphs and let f : V (G) → V (H) be a function. Then the Sierpiński product of G and H with respect to f is defined as a pair (K, ϕ), where K is a graph on the vertex set V (G) × V (H) with two types of edges:. Graph K will be denoted by G ⊗ f H. Function ϕ is needed to define the product of more than two factors. By applying this operation n times to the same graph we obtain the n-th generalized Sierpiński graph. Some basic properties of the Sierpiński product are presented. In particular, we show that G ⊗ f H is connected if and only if both G and H are connected and we present some necessary and sufficient conditions that G, H must fulfill in order for G⊗ f H to be planar. As for symmetry properties, we show which automorphisms of G and H extend to automorphisms of G ⊗ f H. In many cases we can also describe the whole automorphism group of G ⊗ f H.

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Sierpiński graphs as spanning subgraphs of Hanoi graphs

Cited by 8 publications

References 12 publications

The Sierpiński product of graphs

The Sierpiński product of graphs

Sierpiński products of r-uniform hypergraphs

The Sierpiński product of graphs

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