Nilai Total Ketakteraturan Titik dari Honeycomb Network
DOI:
https://doi.org/10.24014/jsms.v6i2.10561Abstract
Topik penelitian ini adalah pelabelan total tak teratur titik pada honeycomb network. Misalkan adalah suatu graf, fungsi * ( ) + disebut pelabelan- total tak teratur titik (vertex irregular total -labeling) pada , jika setiap dua titik yang berbeda di mempunyai bobot yang berbeda. Bobot titik di terhadap fungsi adalah sehingga ( ) ( ) ∑ ( ). Bilangan bulat positif terkecil sedemikian mempunyai suatu pelabelan- total tak teratur titik dinamakan nilai total ketakteraturan titik (total vertex irregularity strength) dari , dilambangkan dengan ( ). Dari hasil penelitian ini diperoleh nilai total ketakteraturan titik dari honeycomb network yang dinotasikan dengan ( ) untuk ( ( )) ⌈ ⌉.
References
Aarthi, S., Stability of Total Vertex Irregularity Strength of Helm Graphs, International Journal of Engineering Science and Computing, 7 (8), 2017. 14599 – 14601.
Ahmad, A., Awan, K.M., Javaid, I., Total Vertex Irregularity Strength of Wheel Related Graphs, Australian Journal of Combinatorics, 51, 2011. 147-156.
Ahmad, A., Baca, M., dan Bashir, Y., Total Vertex Irregularity Strength of Certain Classes of Unicyclic Graphs, Bull. Math. Soc. Sci. Math. Roumanie Tome 57, 105(2), 2014. 147-152..
Al-Mushayt, O., Arshad, A., dan Siddiqui, M.K., Total Vertex Irregularity Strengh of Convex Polytope Graphs, Acta Math. Univ. Comenianae, LXXXII(1), 2013. 29-37.
Anholcer, M., Kalkowski, M., M., Przybylo, J., A New Upper Bound for Total Vertex Irregularity Strength of Graphs, Discrete Mathematics 309, 2009. 6316-6317.
Baca, M., Jendrol, S., Miller, M., Ryan, J., On Irregular Total Labelings, Discrete Math., 307, 2007. 1378-1388.
Bondy, J.A., U.S.R. Murty, Graph Theory with Application, Elsevier Science Publishing Company Inc., New York. 1982.
Gadkaree, K.P., Carbon Honeycomb Structures for Adsorption Applications, Carbon, 36(7), 1998. 981-989.
Gallian, J. A., A Dynamic Survey of Graph Labeling. Electronic Journal of Combinatorics, #DS6. 2016.
Indriati, D., Widodo, Rosyida, I., dan Sugeng, K.A., The Construction of Labeling and Total Irregularity Strength of Specified Caterpilar Graph, Journal of Physics : Conf. Series 855, 2017.
Jeyanthi, P. dan Sudha, A., Total Vertex Irregularity Strength of Some Graphs, Palestine Journal of Mathematics, 7 (2), 2018. 725-733.
Masuda, H. dan Fukuda, K., Ordered Metal Nanohole Arrays Made by a Two-Step Replication of Honeycomb Structures of Anodic Alumina, Science, 268 (5216), 1995. 1466-1468.
Munir, Rinaldi, Matematika Diskrit Edisi Ketiga. Bandung: Penerbit Informatika. 2010.
Nurdin, Baskoro, E.T., Salman, A.N.M., Gaos, N., On the Total Vertex Irregularity Strength of Trees, Discrete Mathematics 310, 2010. 3043-3048.
Nurdin, Baskoro, E.T., Salman, A.N.M., dan Gaos, N.N., On the Total Vertex-Irregular Labelings for Several Types of Trees, Utilitas Math., 82, 2010. 277-290.
Rajasingh, I. dan Arockiamary, S.T., Total Edge Irregularity Strength of Honeycomb Torus Networks, Global Journal of Pure and Applied Mathematics, 13(4), 2017. 1135-1142.
Rajasingh, I., Rajan, B., dan Annamma, V., Total Vertex Irregularity Strength of Circular Ladder and Windmill Graphs, International Conf. on Mathematical Computer Engineering, 2013. 418-423
Ramdani, R., Salman, A.N.M., Assiyatun, H., An Upper Bound on the Total Vertex Irregularity Strength of the Cartesian Product of and an Arbitrary Regular Graph, Procedia Computer Science 74, 2015. 105-111.
Ramdani, R., Salman, A.N.M., Assiyatun H., Semanicova-Fenovcicova, dan Baca, M., On the Total Irregularity Strength of Disjoint Union of Arbitrary Graphs, Math. Reports, 18 (68) 4, 2016. 469-482.
Ramdani, R., dan Ramdhani, M.A., Total Vertex Irregularity Strength of Comb Product of Two Cycles, MATEC Web of Conf. 197, 01007 , 2018.
Sari, M., Nilai Total Ketakteraturan dari Graf Butterfly Network Level 3, skripsi.
Silaban, D.R., Kekaleniate, H., Lutpiah, S., Sugeng, K.A., dan Baskoro, E.T., Algorithm to Construct Graph with Total Vertex Irregularity Strength Two, Procedia Computer Science 74, 2015. 132-137.
Slamin, Dafik, dan Winnona, W., Total Vertex Irregularity Strength of Disjoint Union of Sun Graphs, International Journal of Combinatorics , 2012.
Wallis W.D., Magic Graphs, Boston: Birkhauser. 2001.
Downloads
Published
Issue
Section
License
JSMS : Jurnal Sains Matematika dan Statistika operates an Open Access policy under a Creative Commons Attribution 4.0 International License. Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution 4.0 International License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
