On the partition dimension of a class of circulant graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F14%3A43922051" target="_blank" >RIV/49777513:23520/14:43922051 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0020019014000234" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0020019014000234</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ipl.2014.02.005" target="_blank" >10.1016/j.ipl.2014.02.005</a>

Result language
angličtina
Original language name
On the partition dimension of a class of circulant graphs
Original language description
For a vertex v of a connected graph G=(V,E), a subset S of V and an ordered k-partition Pi={S(1),S(2)...S(k)} of V, the partition representation of v with respect to Pi is the k-vector r(v|Pi)=(d(v,S(1)),d(v,S(2))...d(v,S(k))) (where d(v,S(i)) denotes the distance between v and S). The k-partition Pi is a resolving partition if the k-vectors r(v|Pi) are distinct for all v in V(G). The minimum k for which there is a resolving k-partition of V is the partition dimension of G. Salman et al.[1] in their paper which appeared in Acta Mathematica Sinica, English Series proved that partition dimension of a class of circulant graph G(n,+-{1,2}), for all even n greater than 4, is four. In this paper we prove that the correct value is three.
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)