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Title:On the geodetic number and related metric sets in Cartesian product graphs
Authors:Brešar, Boštjan (Author)
Klavžar, Sandi (Author)
Tepeh, Aleksandra (Author)
Files:URL http://dx.doi.org/10.1016/j.disc.2007.10.007
 
Language:English
Work type:Not categorized (r6)
Typology:1.01 - Original Scientific Article
Organization:FERI - Faculty of Electrical Engineering and Computer Science
Abstract:Množica vozlišč ▫$S$▫ grafa ▫$G$▫ je geodetska množica, če vsako vozlišče grafa ▫$G$▫ leži na vsaj enem intervalu med vozliščema iz ▫$S$▫. Moč najmanjše geodetske množice v ▫$G$▫ imenujemo geodetsko število grafa ▫$G$▫. Dokazana je zgornja meja za geodetsko število kartezičnega produkta in za nekatere razrede grafov je dobljena tudi natančna vrednost. Prav tako je dokazano, da imajo mnoge metrično definirane množice v kartezičnih produktih produktno strukturo in da je konturna množica v kartezičnem produktu geodetska natanko tedaj, ko sta njeni projekciji geodetski množici v faktorjih.
Keywords:matematika, teorija grafov, kartezični produkt, geodetsko število, geodetska množica, konturna množica, mathematics, graph theory, Cartesian product, geodetic number, geodetic set, contour set
Year of publishing:2008
Number of pages:str. 5555-5561
Numbering:Vol. 308, iss. 23
UDC:519.17
ISSN on article:0012-365X
COBISS_ID:14936409 Link is opened in a new window
NUK URN:URN:SI:UM:DK:A1DRLWKP
Views:498
Downloads:77
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Categories:Misc.
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Record is a part of a journal

Title:Discrete Mathematics
Shortened title:Discrete math.
Publisher:North-Holland
ISSN:0012-365X
COBISS.SI-ID:1118479 New window

Secondary language

Language:Unknown
Title:Geodetsko število in sorodne metrične množice v kartezičnih produktih grafov
Abstract:A set ▫$S$▫ of vertices of a graph ▫$G$▫ is a geodetic set if every vertex of ▫$G$▫ lies in at least one interval between the vertices of ▫$S$▫. The size of a minimum geodetic set in ▫$G$▫ is the geodetic number of ▫$G$▫. Upper bounds for the geodetic number of Cartesian product graphs are proved and for several classes exact values are obtained. It is proved that many metrically defined sets in Cartesian products have product structure and that the contour set of a Cartesian product is geodetic if and only if their projections are geodetic sets in factors.


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