The Characterization of Caterpillars with Multidimension 3

Varanoot Khemmani, Supachoke Isariyapalakul

Abstract


Let v be a vertex of a connected graph G, and let W = {w1, w2, ..., wk} be a set of vertices of G. The multirepresentation of v with respect to W is the k-multiset mr(v|W) = {d(v,w1),d(v,w2),...,d(v,wk)}. A set W is called a multiresolving set of G if no two vertices of G have the same multirepresentations with respect to W. The multidimension of G is the minimum cardinality of a multiresolving set of G. In this paper, we characterize the caterpillars with multidimension 3.


Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|