| 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: |  PDF - Presentation file, download (533,30 KB)
MD5: 5B2EE11E73604A9130960C81137B6CF1
 URL - Source URL, visit https://amc-journal.eu/index.php/amc/article/view/1970/1763
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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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 status: | Published |
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| Publication version: | Version of Record |
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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/DiRROS-18479  |
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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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| Note: | Soavtorji: Tomaž Pisanski, Sara Sabrina Zemljič, Arjana Žitnik;
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| Publication date in DiRROS: | 19.03.2024 |
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| Views: | 1268 |
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| Downloads: | 778 |
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