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Title:
On induced and isometric embeddings of graphs into the strong product of paths
Authors:
ID
Jerebic, Janja
(
Author
)
ID
Klavžar, Sandi
(
Author
)
Files:
http://dx.doi.org/10.1016/j.disc.2005.09.019
Language:
English
Work type:
Scientific work
Typology:
1.01 - Original Scientific Article
Organization:
PEF - Faculty of Education
Abstract:
The strong isometric dimension and the adjacent isometric dimension of graphs are compared. The concepts are equivalent for graphs of diameter 2 in which case the problem of determining these dimensions can be reduced to a covering problem with complete bipartite graphs. Using this approach several exact strong and adjacent dimensions are computed (for instance of the Petersen graph) and a positive answer is given to the Problem 4.1 of Fitzpatrick and Nowakowski [The strong isometric dimension of finite reflexive graphs, Discuss. Math. Graph Theory 20 (2000) 23-38] whether there is a graph ▫$G$▫ with the strong isometric dimension bigger that ▫$lceil |V(G)|/2 rceil$▫.
Keywords:
mathematics
,
graph theory
,
strong product of graphs
,
adjacent isometric dimension
,
strong isometric dimension
Publication status:
Published
Publication version:
Version of Record
Publisher:
Elsevier
Year of publishing:
2006
Number of pages:
str. 1358-1363
Numbering:
Letn. 306, št. 13
PID:
20.500.12556/DKUM-51556
UDC:
519.17
ISSN on article:
0012-365X
COBISS.SI-ID:
14028121
NUK URN:
URN:SI:UM:DK:Q2U0POLD
Publication date in DKUM:
10.07.2015
Views:
1352
Downloads:
129
Metadata:
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
Secondary language
Language:
Slovenian
Title:
O induciranih in izometričnih vložitvah grafov v krepke produkte poti
Abstract:
Primerjani sta krepka izometrična dimenzija in sosedna izometrična dimenzija grafov. Koncepta sta ekvivalentna za grafe premera 2 in v tem primeru se problem določitve dimenzije reducira na problem pokritja s polnimi dvodelnimi grafi. S pomočjo tega pristopa je določena krepka izometrična dimenzija in sosedna izometrična dimenzija za različne grafe (na primer za Petersenov graf). Podan je pozitiven odgovor na Problem 4.1 iz [Fitzpatrick, Nowakowski, The strong isometric dimension of finite reflexive graphs, Discuss. Math. Graph Theory 20 (2000) 23-38], ali obstaja tak graf ▫$G$▫, ki ima krepko izometrično dimenzijo večjo od ▫$lceil |V(G)|/2 rceil$▫.
Keywords:
matematika
,
teorija grafov
,
krepki produkt grafov
,
krepka izometrična dimenzija
,
sosedna izometrična dimenzija
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