Some Steiner concepts on lexicographic products of graphs

Anand, Bijo S.; Changat, Manoj; Peterin, Iztok; Narasimha-Shenoi, Prasanth G.

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Title:	Some Steiner concepts on lexicographic products of graphs
Authors:	ID Anand, Bijo S. (Author) ID Changat, Manoj (Author) ID Peterin, Iztok (Author) ID Narasimha-Shenoi, Prasanth G. (Author)
Files:	http://www.imfm.si/preprinti/PDF/01179.pdf
Language:	English
Work type:	Not categorized
Typology:	1.01 - Original Scientific Article
Organization:	FERI - Faculty of Electrical Engineering and Computer Science
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].
Keywords:	teorija grafov, leksikografski produkt, Steinerjeva konveksnost, Steinerjeva množica, Steinerjeva razdalja, graph theory, lexicographic product, Steiner convexity, Steiner set, Steiner distance
Year of publishing:	2012
Number of pages:	str. 1-15
Numbering:	Vol. 50, št. 1179
PID:	20.500.12556/DKUM-52006
UDC:	519.17
ISSN on article:	2232-2094
COBISS.SI-ID:	16322393
NUK URN:	URN:SI:UM:DK:29O5SFB6
Publication date in DKUM:	10.07.2015
Views:	1219
Downloads:	117
Metadata:
Categories:	Misc.
:	ANAND, Bijo S., CHANGAT, Manoj, PETERIN, Iztok and NARASIMHA-SHENOI, Prasanth G., 2012, Some Steiner concepts on lexicographic products of graphs. Preprint series [online]. 2012. Vol. 50, no. 1179, p. 1–15. [Accessed 14 April 2025]. Retrieved from: http://www.imfm.si/preprinti/PDF/01179.pdf Copy citation