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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI Journal of the Indonesian Mathematical Society
Hasmawati Hasmawati
Hasanuddin University
Mathematics

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Dimensi Partisi Graf Hasil Amalgamasi Siklus Hasmawati Hasmawati; Ahmad Syukur Daming; Loeky Haryanto; Budi Nurwahyu
Jurnal Matematika, Statistika dan Komputasi Vol. 16 No. 2 (2020): JMSK, JANUARY, 2020
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (505.939 KB) | DOI: 10.20956/jmsk.v16i2.8062

Abstract

Let be a connected graph G and -partition  of  end . The coordinat  to  is definition . If   for every two vertices in t , then  is a called  k-resolving partition of . The minimum k such that  is a k-resolving partition of  is the partition dimension of  and denoted by . In this paper, we show that the partition dimension for amlagamation of cycle graph  for To proof this results, we was used mathematical induction method. 
Partition Dimension of Dutch Windmill Graph: Dimensi Partisi Graf Kincir Angin Belanda untuk siklus orde besar Hasmawati Hasmawati; Budi Nurwahyu; Ahmad Syukur Daming; Amir Kamal Amir
Jurnal Matematika, Statistika dan Komputasi Vol. 17 No. 3 (2021): May, 2021
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v17i3.13596

Abstract

Let be a connected graph G and -partition of end . The coordinat to is definition . If every twovertex is distinct applies, then is a called partition of . The minimum k for which k-resolving partition of is the partition dimension and denoted with . In this paper, we investigates the partition dimensionfor a large Dutch windmill graph for and . We show that if for some, forany.
Metric Dimension of Graph Join P2 and Pt Loeky Haryanto; Nurdin Nurdin; Hasmawati Hasmawati
Journal of the Indonesian Mathematical Society Volume 25 Number 1 (March 2019)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.25.1.747.75-84

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.
Co-Authors Ahmad Syukur Daming Amir Kamal Amir Budi Nurwahyu Loeky Haryanto Loeky Haryanto Nurdin Nurdin