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The Sierpiński product of graphsKovič, Jurij ...In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let ▫$G, \, H$▫ be graphs and let ▫$f: V(G) \to V(H)$▫ be a function. Then ... the Sierpiński product of graphs ▫$G$▫ and ▫$H$▫ with respect to ▫$f$▫, denoted by ▫$G\otimes_f H$▫, is defined as the graph on the vertex set ▫$V(G) \times V(H)$▫, consisting of ▫$|V(G)|$▫ copies of ▫$H$▫; for every edge ▫$\{g, g'\}$▫ of ▫$G▫$ there is an edge between copies ▫$gH$▫ and ▫$g'H$▫ of form ▫$\{(g, f(g'), (g', f(g))\}$▫. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph ▫$G\otimes_f H$▫ is connected if and only if both graphs ▫$G$▫ and ▫$H$▫ are connected and we present some conditions that ▫$G, \, H$▫ must fulfill for ▫$G\otimes_f H$▫ to be planar. As for symmetry properties, we show which automorphisms of ▫$G$▫ and ▫$H$▫ extend to automorphisms of ▫$G\otimes_f H$▫. In several cases we can also describe the whole automorphism group of the graph ▫$G\otimes_f H$▫. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation ▫$n$▫ times to the same graph we obtain an alternative approach to the well-known ▫$n$▫-th generalized Sierpiński graph.Source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 23, no. 1, 2023, art. P1.01 (25 str.))Type of material - article, component part ; adult, seriousPublish date - 2023Language - englishCOBISS.SI-ID - 143319043
Author
Kovič, Jurij |
Pisanski, Tomaž |
Zemljič, Sara Sabrina |
Žitnik, Arjana
Topics
Sierpiński graphs |
graph products |
connectivity |
planarity |
symmetry |
grafi Sierpińskega |
produkti grafov |
povezanost |
ravninskost |
simetrija
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Author | Kovič, Jurij ... |
Title | The Sierpiński product of graphs |
Publication date | 2022-09-01 |
COBISS.SI-ID | 143319043 |
Publication version in repository | Publisher's version |
Publication licence | Creative Commons Attribution 4.0 International |
Embargo | Immediate publication for public |
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source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 23, no. 1, 2023, art. P1.01 (25 str.))
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Kovič, Jurij | 11234 |
Pisanski, Tomaž | 01941 |
Zemljič, Sara Sabrina | 33306 |
Žitnik, Arjana | 14273 |
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