Infinite Trees with Finite Dimensions

Yusuf Hafidh, Edy Tri Baskoro

2019

Abstract

The properties of graph we consider are metric dimension, partition dimension, and locating-chromatic number. Infinite graphs can have either infinite or finite dimension. Some necessary conditions for an infinite graph with finite metric dimension has been studied in 2012. Infinite graphs with finite metric dimension will also have finite partition dimension and locating-chromatic number. In this paper we find a relation between the partition dimension (locating chromatic number) of an infinite tree with the metric dimensions of its special subtree. We also show that it is possible for an infinite trees with infinite metric dimension to have finite partition dimension (locating-chromatic number).

Paper Citation

in Harvard Style

Hafidh Y. and Baskoro E. (2019). Infinite Trees with Finite Dimensions. In Proceedings of the 1st International MIPAnet Conference on Science and Mathematics - Volume 1: IMC-SciMath, ISBN 978-989-758-556-2, pages 11-13. DOI: 10.5220/0009876300002775

in Bibtex Style

@conference{imc-scimath19,
author={Yusuf Hafidh and Edy Tri Baskoro},
title={Infinite Trees with Finite Dimensions},
booktitle={Proceedings of the 1st International MIPAnet Conference on Science and Mathematics - Volume 1: IMC-SciMath,},
year={2019},
pages={11-13},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0009876300002775},
isbn={978-989-758-556-2},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st International MIPAnet Conference on Science and Mathematics - Volume 1: IMC-SciMath,
TI - Infinite Trees with Finite Dimensions
SN - 978-989-758-556-2
AU - Hafidh Y.
AU - Baskoro E.
PY - 2019
SP - 11
EP - 13
DO - 10.5220/0009876300002775