The Partition Dimension of Daisy Graphs and Its Barbell
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Keywords:
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Partition Dimension, Daisy Graph, Barbell Graph
Abstract
The partition dimension of a graph is determined by minimum number of vertex partitions such that every vertex has different distances to the ordered partitions. A complete graph is very easy to determine its partition dimension because each vertex has the same distance to other vertices. However, what are the partition dimension if a complete graph is modified so that it becomes a daisy graph. In this paper, we discuss the partition dimension of daisy graphs. Next, we will also provide barbell graph operations on daisy graphs.
References
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Amrullah, S. Azmi, H. Soeprianto, M. Turmuzi, and Y. S. Anwar (2019). The Partition Dimension of Subdivision Graph on the Star. Journal of Physics: Conference Series, 1280(2); 022037.
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Asmiati, I. K. S. G. Yana, and L. Yulianti (2018). On the Locating Chromatic Number of Certain Barbell Graphs. International Journal of Mathematics and Mathematical Sciences, 2018; 1–5.
Azeem, M., M. Imran, and M. F. Nadeem (2022). Sharp Bounds on Partition Dimension of Hexagonal Möbius Ladder. Journal of King Saud University - Science, 34(2); 101179.
Bagus, K. I. and E. T. Baskoro (2015). Partition Dimension of Some Classes of Trees. Procedia Computer Science, 74; 67–72.
Baskoro, E. T. and D. O. Haryeni (2020). All Graphs of Order n ≥ 11 and Diameter 2 with Partition Dimension n − 3. Heliyon, 6; e03694.
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Chartrand, G., E. Salehi, and P. Zhang (2000). The Partition Dimension of a Graph. Aequationes Mathematicae, 59; 45–54.
Fernau, H., J. A. Rodriguez-Velazquez, and I. G. Yero (2014). On the Partition Dimension of Unicyclic Graphs. Bulletin of the Mathematical Society of the Sciences of Mathematics Roumanie, 105; 381–391.
Fredlina, K. Q. and E. T. Baskoro (2015). The Partition Dimension of Some Families of Trees. Procedia Computer Science, 74; 60–66.
Grigorious, C., S. Stephen, B. Rajan, M. Miller, and A. William (2014). On the Partition Dimension of a Class of Circulant Graphs. Information Processing Letters, 114; 353–356.
Hafidh, Y. and E. T. Baskoro (2024). Partition Dimension of Trees: Palm Approach. Electronic Journal of Graph Theory and Applications, 12(2); 265–272.
Haryeni, D. O., E. T. Baskoro, and S. W. Saputro (2017). On the Partition Dimension of Disconnected Graphs. Journal of Mathematics and Fundamental Sciences, 49; 18–32.
Haryeni, D. O., E. T. Baskoro, and S. W. Saputro (2019). A Method to Construct Graphs with Certain Partition Dimension. Electronic Journal of Graph Theory and Applications, 7(2); 251–263.
Hernando, C., M. Mora, and I. M. Pelayo (2019). Resolving Dominating Partitions in Graphs. Discrete Applied Mathematics, 266; 237–251.
Khali, A., S. K. S. Husain, and M. F. Nadeem (2021). On Bounded Partition Dimension of Different Families of Convex Polytopes with Pendant Edges. AIMS Mathematics, 7(3); 4405–4415.
Koam, A. N. A., A. Khalil, A. Ahmad, and M. Azeem (2024). Cardinality Bounds on Subsets in the Partition Resolving Set for Complex Convex Polytope-Like Graph. AIMS Mathematics, 9(4); 10078–10094.
Kuziak, D., E. Maritz, T. Vetrik, and I. G. Yero (2023). The Edge Partition Dimension of Graphs. Discrete Mathematics Letters, 12; 34–39.
Maritz, E. C. M. and T. Vetrik (2018). The Partition Dimension of Circulant Graphs. Quaestiones Mathematicae, 41; 49–63.
Mohan, C. M., S. Santhakumar, M. Arockiaraj, and J. B. Liu (2019). Partition Dimension of Certain Classes of Series Parallel Graphs. Theoretical Computer Science, 778; 47–60.
Ridwan, M., H. Assiyatun, and E. T. Baskoro (2023). The Dominating Partition Dimension and Locating Chromatic Number of Graphs. Electronic Journal of Graph Theory and Applications, 11(2); 455–465.
Rodríguez-Velazquez, J. A., I. G. Yero, and M. Lemanska (2014). On the Partition Dimension of Trees. Discrete Applied Mathematics, 166; 204–209.
Sugeng, K. A., P. John, M. L. Lawrence, L. F. Anwar, M. Baca, and A. Semanicova-Fenovcikova (2022). Modular Irregularity Strength on Some Flower Graphs. Electronic Journal of Graph Theory and Applications, 11; 27–38.
Amrullah, S. Azmi, H. Soeprianto, M. Turmuzi, and Y. S. Anwar (2019). The Partition Dimension of Subdivision Graph on the Star. Journal of Physics: Conference Series, 1280(2); 022037.
Amrullah, E. T. Baskoro, Simanjuntak, and S. Uttunggadewa (2015). The Partition Dimension of a Subdivision of a Complete Graph. Procedia Computer Science, 74; 53–59.
Asmiati (2012). Partition Dimension of Amalgamation of Stars. Bulletin of Mathematics, 4; 161–167.
Asmiati, I. K. S. G. Yana, and L. Yulianti (2018). On the Locating Chromatic Number of Certain Barbell Graphs. International Journal of Mathematics and Mathematical Sciences, 2018; 1–5.
Azeem, M., M. Imran, and M. F. Nadeem (2022). Sharp Bounds on Partition Dimension of Hexagonal Möbius Ladder. Journal of King Saud University - Science, 34(2); 101179.
Bagus, K. I. and E. T. Baskoro (2015). Partition Dimension of Some Classes of Trees. Procedia Computer Science, 74; 67–72.
Baskoro, E. T. and D. O. Haryeni (2020). All Graphs of Order n ≥ 11 and Diameter 2 with Partition Dimension n − 3. Heliyon, 6; e03694.
Bhatti, R., M. K. Jamil, M. Azeem, and P. Poojary (2024). Partition Dimension of Generalized Hexagonal Cellular Networks and Its Application. IEEE Access, 12; 12199–12208.
Chartrand, G., E. Salehi, and P. Zhang (2000). The Partition Dimension of a Graph. Aequationes Mathematicae, 59; 45–54.
Fernau, H., J. A. Rodriguez-Velazquez, and I. G. Yero (2014). On the Partition Dimension of Unicyclic Graphs. Bulletin of the Mathematical Society of the Sciences of Mathematics Roumanie, 105; 381–391.
Fredlina, K. Q. and E. T. Baskoro (2015). The Partition Dimension of Some Families of Trees. Procedia Computer Science, 74; 60–66.
Grigorious, C., S. Stephen, B. Rajan, M. Miller, and A. William (2014). On the Partition Dimension of a Class of Circulant Graphs. Information Processing Letters, 114; 353–356.
Hafidh, Y. and E. T. Baskoro (2024). Partition Dimension of Trees: Palm Approach. Electronic Journal of Graph Theory and Applications, 12(2); 265–272.
Haryeni, D. O., E. T. Baskoro, and S. W. Saputro (2017). On the Partition Dimension of Disconnected Graphs. Journal of Mathematics and Fundamental Sciences, 49; 18–32.
Haryeni, D. O., E. T. Baskoro, and S. W. Saputro (2019). A Method to Construct Graphs with Certain Partition Dimension. Electronic Journal of Graph Theory and Applications, 7(2); 251–263.
Hernando, C., M. Mora, and I. M. Pelayo (2019). Resolving Dominating Partitions in Graphs. Discrete Applied Mathematics, 266; 237–251.
Khali, A., S. K. S. Husain, and M. F. Nadeem (2021). On Bounded Partition Dimension of Different Families of Convex Polytopes with Pendant Edges. AIMS Mathematics, 7(3); 4405–4415.
Koam, A. N. A., A. Khalil, A. Ahmad, and M. Azeem (2024). Cardinality Bounds on Subsets in the Partition Resolving Set for Complex Convex Polytope-Like Graph. AIMS Mathematics, 9(4); 10078–10094.
Kuziak, D., E. Maritz, T. Vetrik, and I. G. Yero (2023). The Edge Partition Dimension of Graphs. Discrete Mathematics Letters, 12; 34–39.
Maritz, E. C. M. and T. Vetrik (2018). The Partition Dimension of Circulant Graphs. Quaestiones Mathematicae, 41; 49–63.
Mohan, C. M., S. Santhakumar, M. Arockiaraj, and J. B. Liu (2019). Partition Dimension of Certain Classes of Series Parallel Graphs. Theoretical Computer Science, 778; 47–60.
Ridwan, M., H. Assiyatun, and E. T. Baskoro (2023). The Dominating Partition Dimension and Locating Chromatic Number of Graphs. Electronic Journal of Graph Theory and Applications, 11(2); 455–465.
Rodríguez-Velazquez, J. A., I. G. Yero, and M. Lemanska (2014). On the Partition Dimension of Trees. Discrete Applied Mathematics, 166; 204–209.
Sugeng, K. A., P. John, M. L. Lawrence, L. F. Anwar, M. Baca, and A. Semanicova-Fenovcikova (2022). Modular Irregularity Strength on Some Flower Graphs. Electronic Journal of Graph Theory and Applications, 11; 27–38.
Authors
Asmiati, Rachmawati, A. A. ., Nurvazly, D. E. ., & Hamzah, . N. (2025). The Partition Dimension of Daisy Graphs and Its Barbell. Science and Technology Indonesia, 10(2), 313–319. https://doi.org/10.26554/sti.2025.10.2.313-319
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