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Title:The distinguishing number of Cartesian products of complete graphs
Authors:ID Imrich, Wilfried (Author)
ID Jerebic, Janja (Author)
ID Klavžar, Sandi (Author)
Files:URL http://dx.doi.org/doi:10.1016/j.ejc.2007.11.018
 
Language:English
Work type:Article
Typology:1.08 - Published Scientific Conference Contribution
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Razlikovalno število D(G) grafa G je najmanjše število d, tako da G premore označitev z d oznakami, ki jo ohranja le trivialni avtomorfizem. Dokažemo, da lahko kartezične produkte relativno tujih grafov, katerih velikosti se ne razlikujejo preveč, razlikujemo z majhnim številom barv. Za vse k in n določimo razlikovalno število kartezičnega produkta KksquareKk in sicer bodisi eksplicitno, bodisi s kratko rekurzijo. Vpeljemo tudi stolpčno-invariantne množice vektorjev in dokažemo preklopno lemo, ki igra ključno vlogo v dokazih.
Keywords:matematika, teorija grafov, razlikovalno število, polni grafi, kartezični produkt grafov, mathematics, graph theory, distingushing number, complete graphs, Cartesian product
Publication status:Published
Publication version:Version of Record
Year of publishing:2008
Number of pages:Str. 922-929
PID:20.500.12556/DKUM-51670 New window
UDC:519.17
ISSN on article:0195-6698
COBISS.SI-ID:14626905 New window
NUK URN:URN:SI:UM:DK:HHXKS69U
Publication date in DKUM:10.07.2015
Views:1121
Downloads:78
Metadata:XML DC-XML DC-RDF
Categories:Misc.
:
IMRICH, Wilfried, JEREBIC, Janja and KLAVŽAR, Sandi, 2008, The distinguishing number of Cartesian products of complete graphs. In : Homomorphisms: Structure and Highlights [online]. Published Scientific Conference Contribution. 2008. p. 922–929. [Accessed 27 March 2025]. Retrieved from: http://dx.doi.org/doi:10.1016/j.ejc.2007.11.018
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Record is a part of a proceedings

Title:Homomorphisms: Structure and Highlights
COBISS.SI-ID:14626649 New window

Record is a part of a journal

Title:European journal of combinatorics
Shortened title:Eur. j. comb.
Publisher:Academic Press
ISSN:0195-6698
COBISS.SI-ID:25427968 New window

Secondary language

Language:Slovenian
Title:Razlikovalno število kartezičnih produktov polnih grafov
Abstract:The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d labels that is preserved only by a trivial automorphism. We prove that Cartesian products of relatively prime graphs whose sizes do not differ too much can be distinguished with a small number of colors. We determine the distinguishing number of the Cartesian product KksquareKk forall k and n, either explicitly or by a short recursion. We also introduce column-invariant sets of vectors and prove a switching lemma that plays a key role in the proofs.


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