| Title: | Some Steiner concepts on lexicographic products of graphs |
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| Authors: | ID Anand, Bijo S. (Author)
ID Changat, Manoj (Author)
ID Peterin, Iztok (Author)
ID Narasimha-Shenoi, Prasanth G. (Author) |
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| Files: |  http://www.imfm.si/preprinti/PDF/01179.pdf
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FERI - Faculty of Electrical Engineering and Computer Science
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| Abstract: | The smallest tree that contains all vertices of a subset ▫$W$▫ of ▫$V(G)$▫ is called a Steiner tree. The number of edges of such a tree is the Steiner distance of ▫$W$▫ and union of all Steiner trees of ▫$W$▫ form a Steiner interval. Both of them are described for the lexicographic product in the present work. We also give a complete answer for the following invariants with respect to the Steiner convexity: the Steiner number, the rank, the hull number, and the Carathéodory number, and a partial answer for the Radon number. At the end we locate and repair a small mistake from [J. Cáceres, C. Hernando, M. Mora, I. M. Pelayo, M. L. Puertas, On the geodetic and the hull numbers in strong product graphs, Comput. Math. Appl. 60 (2010) 3020--3031]. |
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| Keywords: | teorija grafov, leksikografski produkt, Steinerjeva konveksnost, Steinerjeva množica, Steinerjeva razdalja, graph theory, lexicographic product, Steiner convexity, Steiner set, Steiner distance |
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| Year of publishing: | 2012 |
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| Number of pages: | str. 1-15 |
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| Numbering: | Vol. 50, št. 1179 |
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| PID: | 20.500.12556/DKUM-52006  |
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| UDC: | 519.17 |
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| ISSN on article: | 2232-2094 |
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| COBISS.SI-ID: | 16322393 |
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| NUK URN: | URN:SI:UM:DK:29O5SFB6 |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 1362 |
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| Downloads: | 128 |
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| Metadata: |    |
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| Categories: | Misc.
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