DIMENSI METRIK GRAF DAN APLIKASINYA PADA PEMASANGAN SENSOR KEBAKARAN
DOI:
https://doi.org/10.12928/admathedu.v12i1.20604Keywords:
Graf, Dimensi Metrik, Himpunan Pembeda.Abstract
Himpunan pembeda adalah himpunan bagian dari titik-titik pada sebuah graf terhubung yang dapat memberikan koordinat berbeda kepada setiap titik pada graf tersebut. Suatu graf dapat memiliki lebih dari satu himpunan pembeda. Himpunan pembeda dengan jumlah anggota minimum disebut himpunan pembeda minimum, dan kardinalitas dari himpunan pembeda minimum disebut dimensi metrik dari graf tersebut. Salah satu bentuk pengaplikasian dari konsep dimensi metrik pada kehidupan sehari-hari adalah dalam pemasangan sensor kebakaran di sebuah gedung. Pada tulisan ini akan diterapkan konsep dimensi metrik pada pemasangan sensor kebakaran di Gedung Utama Kampus III Universitas Sanata Dharma untuk mendapat jumlah sensor dan letak pemasangan yang optimal.
References
Pustaka
Al-Ammori, A., et al. (2019). Probabilistic-mathematical models for formation of information flows in aircraft fire alarm system. Journal of Automation and Information Sciences, 51 (7): 67-80.
Chartrand, G. et al. (2000). Resolvability in graphs and the metric dimension of a graph. Discrete Applied Mathematics, 105 (1-3): 99-113.
Cheng, J. C. P., et al. (2021). Graph-based network generation and CCTV processing techniques for fire evacuation. Building Research & Information, 49 (2): 179-196.
Eka, S. & Rahadjeng, B. (2013). Dimensi Metrik Pada Graf Lintasan, Graf Komplit, Graf Sikel, Graf Bintang, dan Graf Bipartit Komplit. Skripsi. Surabaya: Jurusan Matematika, Universitas Negeri Surabaya.
Epp, S. S. (2011). Discrete Mathematics with Applications (Fourth Edition). Boston: Brooks/Cole.
Kadir, E. A., et al. (2019). Multi-sensor system for land and forest fire detection application in Peatland area. Indonesian Journal of Electrical Engineering and Informatics, 7 (4): 789-799.
Morgan, M., et al. (2011). On the eccentric connectivity index of a graph. Discrete Mathematics, 311 (13): 1229-1234.
Udahemuka, G., et al. (2020). Characterization of background temperature dynamics of a multitemporal satellite scene through data assimilation for wildfire detection. Remote Sensing, 12 (10): 1661.
Zheng, Y., et al. (2007). Localization using boundary sensors: An analysis based on graph theory. ACM Transactions on Sensor Networks, 3 (4): 21-es.
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