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Title:The strong isometric dimension of graphs of diameter two
Authors:ID Jerebic, Janja (Author)
ID Klavžar, Sandi (Author)
Files:URL http://www.imfm.si/preprinti/PDF/00876.pdf
 
Language:English
Work type:Not categorized
Organization:PEF - Faculty of Education
Abstract:Krepka izometrična dimenzija ▫$textrm{idim}(G)$▫ grafa ▫$G$▫ je najmanjše število ▫$k$▫, za katero lahko ▫$G$▫ izometrično vložimo v krepki produkt ▫$k$▫ poti. Problem določitve ▫$textrm{idim}(G)$▫ za grafe premera dva je reduciran na problem pokrivanja komplementa grafa ▫$G$▫ s polnimi dvodelnimi grafi. Za primer je pokazano, da je izometrična dimenzija Petersenovega grafa enaka 5.
Keywords:matematika, teorija grafov, izometrični podgraf, krepki produkt grafov, premer grafa, krepka izometrična dimenzija, Petersenov graf, mathematics, graph theory, isometric subgraph, strong product of graphs, graph diameter, strong isometric dimension, Petersen graph
Year of publishing:2003
Number of pages:str. 1-8
Numbering:Vol. 41, št. 876
PID:20.500.12556/DKUM-49367 New window
ISSN:1318-4865
UDC:519.17
COBISS.SI-ID:12396377 New window
NUK URN:URN:SI:UM:DK:NRNPR4FM
Publication date in DKUM:10.07.2015
Views:1566
Downloads:84
Metadata:XML DC-XML DC-RDF
Categories:Misc.
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Secondary language

Language:Unknown
Title:Krepka izometrična dimenzija grafov premera dva
Abstract:The strong isometric dimension ▫$textrm{idim}(G)$▫ of a graph ▫$G$▫ is the least number ▫$k$▫ such that ▫$G$▫ can be isometrically embedded into the strong product of ▫$k$▫ paths. The problem of determining ▫$textrm{idim}(G)$▫ for graphs of diameter two is reduced to a covering problem of the complement of ▫$G$▫ with complete bipartite graphs. As an example it is shown that ▫$textrm{idim}(P) = 5$▫, where ▫$P$▫ is the Petersen graph.


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