| Title: | Resolvability and convexity properties in the Sierpiński product of graphs |
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| Authors: | ID Henning, Michael A. (Author)
ID Klavžar, Sandi (Author)
ID Yero, Ismael G. (Author) |
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| Files: |  URL - Source URL, visit https://link.springer.com/article/10.1007/s00009-023-02544-6
 PDF - Presentation file, download (432,07 KB)
MD5: 074DE5ECE31FEB8F337B464DEC07BA72
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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: | Let $G$ and $H$ be graphs and let $f \colon V(G)\rightarrow V(H)$ be a function. The Sierpiński product of $G$ 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 $gg'$ 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 $(g,f(g'))(g',f(g))$. The Sierpiński metric dimension and the upper Sierpiński metric dimension of two graphs are determined. Closed formulas are determined for Sierpiński products of trees, and for Sierpiński products of two cycles where the second factor is a triangle. We also prove that the layers with respect to the second factor in a Sierpiński product graph are convex. |
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| Keywords: | Sierpiński product of graphs, metric dimension, trees, convex subgraph |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 17 str. |
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| Numbering: | Vol. 21, iss. 1, article no. 3 |
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| PID: | 20.500.12556/DiRROS-18195  |
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| UDC: | 519.17 |
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| ISSN on article: | 1660-5446 |
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| DOI: | 10.1007/s00009-023-02544-6 |
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| COBISS.SI-ID: | 172901379 |
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| Note: | Spletna objava: 18. 11. 2023;
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| Publication date in DiRROS: | 16.02.2024 |
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| Views: | 142 |
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| Downloads: | 60 |
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