| Title: | The Sierpiński product of graphs |
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| Authors: | ID Kovič, Jurij (Author)
ID Pisanski, Tomaž (Author)
ID Zemljič, Sara Sabrina (Author)
ID Žitnik, Arjana (Author) |
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| Files: |  AMC_Kovic_Pisanski_Zemljic_Zitnik_i2022.pdf (526,44 KB)
MD5: 4877F5DF98ECDA9B5FD0C4CCEE915376
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | 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. |
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| Keywords: | Sierpiński graphs, graph products, connectivity, planarity, symmetry |
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| Publication date: | 01.01.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | art. P1.01 (25 str.) |
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| Numbering: | Vol. 23, no. 1 |
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| PID: | 20.500.12556/RUP-19869-db236bc0-7b5f-0e1b-342e-58c3685a1410  |
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| UDC: | 519.17 |
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| ISSN on article: | 1855-3966 |
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| DOI: | 10.26493/1855-3974.1970.29e |
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| COBISS.SI-ID: | 143319043 |
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| Publication date in RUP: | 06.11.2023 |
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| Views: | 1906 |
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| Downloads: | 4 |
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| Metadata: |    |
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