# METRIC DIMENSION OF GRAPH JOIN TWO PATHS P2AND Pt
> Haryanto L.

URL kanonis: https://discover.unhas.ac.id/publications/metric-dimension-of-graph-join-two-paths-p2and-pt
Jurnal / Konferensi: Journal of the Indonesian Mathematical Society
Tahun terbit: 2019
DOI: https://doi.org/10.22342/JIMS.25.1.747.75-84
ISSN: 20868952
Kuartil SJR: Q3
Citations: 2

## Authors
- Haryanto L.

## Abstract
The following metric dimension of join two paths $P_2 + P_t$ is determined as follows. For every $k = 1, 2, 3, ...$ and $t = 2 + 5k$ or $t = 3 + 5k$, the dimension of $P_2 + P_t$ is $2 + 2k$ whereas for $t = 4 + 5k, t = 5(k+1)$ or $t = 1 + 5(k+1)$, the dimension is $3 + 2k$. In case $t \geq 7$, the dimension is determined by a chosen (maximal) ordered basis for $P_2 + P_t$ in which the integers 1, 2 are the two consecutive vertices of $P_2$ and the next integers $3, 4, ..., t + 2$ are the $t$ consecutive vertices of $P_t$. If $t \geq 10$, the ordered binary string contains repeated substrings of length 5. For $t < 7$, the dimension is easily found using a computer search, or even just using hand computations.

## Keywords
- Mathematics
- Combinatorics
- Dimension (graph theory)
- Join (topology)
- Graph
- Substring
- Metric dimension
- Discrete mathematics
- Set (abstract data type)
- Pathwidth
- Line graph
- Computer science
- Programming language

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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