DIMENSI PARTISI GRAF HASIL OPERASI COMB GRAF LINGKARAN DAN GRAF LINTASAN

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Published: Dec 31, 2019
DOI: https://doi.org/10.24853/fbc.5.2.163-174
Keywords:
Dimensi metrik Dimensi Partisi Graf Comb Partisi Pembeda

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Faisal Faisal
Departemen Matematika, School of Computer Science, Universitas Bina Nusantara
Novi Mardiana
Program Studi Teknik Informatika, STMIK IKMI Cirebon
Hastri Rosiyanti
Pendidikan Matematika, Fakultas Ilmu Pendidikan, Universitas Muhammadiyah Jakarta

Abstract

Dimensi partisi adalah perluasan dari konsep dimensi metrik. Konsep dimensi partisi pertama kali diperkenalkan oleh Chartrand pada tahun 1998 (Chartrand,1998). Partisi Π dari himpunan titik V(G) adalah suatu partisi pembeda  dari G, yaitu jika setiap dua verteks yang berbeda dari graf G dapat dibedakan oleh vektor dengan koordinatnya adalah jarak terhadap elemen-elemen di Π. Dimensi partisi dari graf G, dinotasikan pd(G) adalah partisi pembeda dari G dengan kardinalitas paling minimum. Pada artikel ini, graf yang dikaji adalah graf yang diperoleh dari hasil operasi comb antara dua graf terhubung yaitu graf Lingkaran Cn  dan Lintasan Pk. Misalkan o adalah suatu titik dari Pk. Operasi comb antara Cn  dan Pk  adalah graf yang diperoleh dengan mengambil 1 graf Cn  dan |V(Cn)| buah graf Pk  dan menempelkan titik o  dari Pk  pada titik ke-i dari Cn. Kami menyajikan hasi bahwa dimensi partisi dari graf operasi comb antara Cn dan Pk  sama dengan dimensi partisi graf Cn  dimana o adalah titik berderajat 1. Disajikan juga konjektur bahwa dimensi partisi dari graf operasi com antara graf G dan Pk  sama dengan dimensi partisi graf G dimana o titik berderajat 1  untuk graf  G sebarang.

Article Details

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Vol. 5 No. 2 (2019): FIBONACCI: Jurnal Pendidikan Matematika dan Matematika
Section
Articles

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References

Accardi, L., dkk. 2004. “Monotone independence, comb graphs and Bose-Einstein condensation”. Infinite Dimensional Analysis, Quantum Probability and Related Topics. Vol 7 (3), pp: 419-435.

Alfarisi, R. dan Darmaji. 2017a. “ On the partition dimension of comb product of path and complete graph”. AIP Conference Proceedings. Vol 1867 (1).

Alfarisi, R., dkk. 2017b. “On the star partition dimension of comb product of cycle and path”. AIP Conference Proceedings. Vol. 1867.

Alfarisi, R., dkk. 2017c. “On the star partition dimension of comb product of cycle and complete graph”. Journal of Physics : Conference Series. Vol. 855.

Alfarisi, R. 2017d. The Partition dimension and star partition dimension of comb product of two connected graphs. Thesis. Surabaya: ITS.

Balaban, A. T. 1985. “Application of Graph Theory in Chemistry”. Journal of Chemical Information and Computer Sciences. Vol. 25 (3), pp: 334-3

Chartrand, G., dkk. 2000. “The partition dimension of a graph”. Aequationes mathematicae. Vol 59 (1-2), pp: 45-54.

Chartrand, G., dkk, 1998. “On the partition dimension of graph”. Congressus Numerantium. Vol 130, pp:157-168.

Fehr, M., dkk. 2006. “The partition dimension of Cayley digraphs”. Aequationes mathematicae. Vol 71 (1-2), pp: 1-18.

Godsil, H. D., dan Mckay, B. D. 1978. “ A new graph product and its spectrum”. Bulletin of the Australian Mathematical Society. Vol 18 (1), pp: 21-28.

Grigorius, C., dkk. 2014. “On the partition dimension of a class of circulant graphs”. Journal Information Processing Letters. Vol 114 (7), pp: 353-356.

Harary, F. 1959. “Graph theory and electric networks”. IRE Transactions On Circuit Theory. Vol 6 (5), pp: 95-109

Haryeni, D. O., dkk. 2017. “On the partition dimension of disconnected graphs”. Journal of Mathematical and Fundamental Sciences. Vol 49 (1), pp 18-32.

Hora, A., dan Obata, N. 2007. Comb graphs and star graphs. In: Quantum Probability and Spectral Analysis of Graphs. Theoretical and Mathematical Physics. Berlin, Heidelberg: Springer.

Rodri ́guez, A. J., dkk. 2014. “On the partition dimension of trees”. Discrete Applied Mathematics. Vol 166, pp: 204-209.

Rodri ́guez, A. J., dkk. 2014. “The partition dimension of corona product graphs”. https://arxiv.org/abs/1010.5144 diakses pada 19 Desember 2019

Roth, J., dan Hashimshony, R. 1988. “Algorithms in graph theory and their use for solving problems in architectural design”. Computer-Aided Design. Vol. 20 (7), pp: 373-381.

Singh, R. P. dan Vandana. 2014. “Application of Graph Theory in Computer Science and Engineering”. International Journal of Computer Application. Vol. 104(1), pp:10-13.

Scarselli, F., dkk. 2009. “The graph Neural Network”. IEEE Transactions on Neural Networks. Vol 20 (1), pp: 61-80.

Saputro, S. W., dkk. 2017. The metric dimension of comb product graphs. Matematick Vesnik. Vol 69 (4)

Yap, I. V., dkk. 2003. “A Graph-Theoretic Approach to Comparing and Integrating Genetic”. Physical and Sequence-Based Maps. Vol. 165 (4), pp: 2235-2247.

Yero, I. G., dkk. 2014. “ The partition dimension of strong product graphs and Cartesian product graphs”. Discrete Mathematics. Vol 331, pp:43-52.