On the geodetic number and related metric sets in Cartesian product graphs

Brešar, Boštjan; Klavžar, Sandi; Tepeh, Aleksandra

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Title:	On the geodetic number and related metric sets in Cartesian product graphs
Authors:	ID Brešar, Boštjan (Author) ID Klavžar, Sandi (Author) ID Tepeh, Aleksandra (Author)
Files:	http://dx.doi.org/10.1016/j.disc.2007.10.007
Language:	English
Work type:	Not categorized
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
PID:	20.500.12556/DKUM-51752
UDC:	519.17
ISSN on article:	0012-365X
COBISS.SI-ID:	14936409
NUK URN:	URN:SI:UM:DK:A1DRLWKP
Publication date in DKUM:	10.07.2015
Views:	1036
Downloads:	109
Metadata:
Categories:	Misc.
:	BREŠAR, Boštjan, KLAVŽAR, Sandi and TEPEH, Aleksandra, 2008, On the geodetic number and related metric sets in Cartesian product graphs. Discrete mathematics [online]. 2008. Vol. 308, no. 23, p. 5555–5561. [Accessed 31 March 2025]. Retrieved from: http://dx.doi.org/10.1016/j.disc.2007.10.007 Copy citation

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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

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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