Determining The Number of Connected Vertex Labeled Graphs of Order Seven without Loops by Observing The Patterns of Formula for Lower Order Graphs with Similar Property
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Keywords:
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Graph, Connected, Vertex, Labeled, Order, Loops
Abstract
Given n vertices and m edges, m ≥ 1, and for every vertex is given a label, there are lots of graphs that can be obtained. The graphs obtained may be simple or not simple, connected or disconnected. A graph G(V,E) is called simple if G(V,E) not containing loops nor paralel edges. An edge which has the same end vertex is called a loop, and paralel edges are two or more edges which connect the same set of vertices. Let N(G7,m,t) as the number of connected vertex labeled graphs of order seven with m vertices and t (t is the number edges that connect different pair of vertices). The result shows that N(G7,m,t) = ct C (m−1) t−1, with c6=6727, c7=30160 , c8=30765, c9=21000, c10=28364, c11=26880, c12=26460, c13=20790, c14=10290, c15= 8022, c16=2940, c17=4417, c18=2835, c19=210, c20= 21, c21=1.
References
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Disconnected Vertices Labeled Graphs of Order Six with the Maximum Number Twenty Parallel Edges and Containing No Loops. Journal of Physics: Conference Series 1751 (01), 012024. doi:10.1088/1742-6596/1751/1/012024
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Wamiliana, A. Nuryaman, Amanto, A. Sutrisno, and N. A. Prayoga. (2019). Determining the Number of Connected Vertices Labeled Graph of Order Five with Maximum Number of Parallel Edges is Five and Containing No Loops. IOP Conf. Series: Journal of Physics: Conf. Series 1338 (2019) 012043. doi:10.1088/1742-6596/1338/1/012043
Wamiliana, Amanto and Nagari G.T. (2016). Counting the Number of Disconnected Labeled Graphs of Order Five without Parallel Edges International Series on Interdisciplinary Sciences and Technology (INSIST) Vol 1 (1) p 1-6.
Al Etaiwi, W. M. (2014). Encryption Algorithm Using Graph Theory. Journal of Scientific Research and Reports 3 (19): 2519-2527
Álvarez, M. C.; Ehnts, D. (2015). The roads not taken: Graph theory and macroeconomic regimes in stock-flow consistent modeling, Working Paper, No. 854, Levy Economics Institute of Bard College, Annandale-on-Hudson, NY
Baizhu N., Rabiha Q., Shafiq U.R, Ghulam F. (2021). Some Graph-Based Encryption Schemes. Journal of Mathematics, Vol 2021, pp. 1-8. https://doi.org/10.1155/2021/6614172
Brandes, U. and Cornelsen S. (2009). Phylogenetic graph models beyond trees. Discrete Applied Mathematics, 157(10); 2361–2369
Bóna, M. (2007). Introduction to Enumerative Combinatorics. McGraw Hill Inc. New York
Cayley, A. (1874) On the Mathematical Theory of Isomers’, Philosophical Magazine, vol. 47, no. 4, 1874, pp.444 – 446.
Gramatica R, Di Matteo T, Giorgetti S, Barbiani M, Bevec D, Aste T. (2014). Graph Theory Enables Drug Repurposing – How a Mathematical Model Can Drive the Discovery of Hidden Mechanisms of Action. PLoS ONE 9(1): e84912. https://doi.org/10.1371/journal.pone.0084912
Hsu L. H., and Lin C.K. (2009). Graph Theory and Interconnection Network. Taylor and Francis Group, LLC, New York.
Huson D. H., and Bryant D. (2006). Application of Phylogenetic Networks in Evolutionary Studies. Molecular Biology and Evolution, vol. 23, Issue 2, pp. 254–267, https://doi.org/10.1093/molbev/msj030
Kawakura S., and Shibasaki R. (2018). Grouping Method Using Graph Theory for Agricultural Workers Engaging in Manual Tasks. Journal of Advanced Agricultural Technologies 5 (3) pp. 173 -181. doi: 10.18178/joaat.5.3.173-181
Kannimuthu, S., Bhanu, D., Bhuvaneshwari, K.S. (2020). A novel approach for agricultural decision making using graph coloring. SN Applied Sci. Vol. 2 (1), 31. https://doi.org/10.1007//s42452-019-1847-8
Mathur R. and Adlakha N. (2016). A graph theoretic model for prediction of reticulation events and phylogenetic networks for DNA sequences. Egyptian Journal of Basic and Applied Sciences 3(3) p 263-271 doi: 10.1016/j.ejbas.2016.07.004
Pertiwi, F. A, Amanto, Wamiliana, Asmiati, Notiragayu, (2021). Calculating the Number of vertices Labeled Order Six Disconnected Graphs which Contain Maximum Seven Loops and Even Number of Non-loop Edges Without Parallel Edges. Journal of Physics: Conference Series 1751 (01), 012026. doi:10.1088/1742-6596/1751/1/012026
Priyadarsini P.L.K. (2015). A Survey on some Applications of Graph Theory in Cryptography. Journal of Discrete Mathematical Sciences and Cryptography, 18:3, 209-217
Puri, F.C., Wamiliana., Usman, M., Amanto., Ansori, M., Antoni, Y. (2021). The Formula to Count the Number of Vertices Labeled Order Six Connected Graphs with Maximum Thirty Edges without Loops. Journal of Physics: Conference Series 1751 (01), 012023.
Putri, D., Wamiliana, Fitriani, Faisol A, Dewi K. S. (2021). Determining the Number of
Disconnected Vertices Labeled Graphs of Order Six with the Maximum Number Twenty Parallel Edges and Containing No Loops. Journal of Physics: Conference Series 1751 (01), 012024. doi:10.1088/1742-6596/1751/1/012024
Slomenski, W.F. (1964). Application of the Theory of Graph to Calculations of the Additive Structural Properties of Hydrocarbon. Russian Journal of Physical Chemistry, vol. 38, 1964, pp.700-703
Wamiliana, Amanto, Usman, M., Ansori, M., Puri, F.C. (2020). Enumerating the Number of Connected Vertices Labeled Graph of Order Six with Maximum Ten Loops and Containing No Parallel Edges. Science and Technology Indonesia 5 (4), 131-135.
Wamiliana, A. Nuryaman, Amanto, A. Sutrisno, and N. A. Prayoga. (2019). Determining the Number of Connected Vertices Labeled Graph of Order Five with Maximum Number of Parallel Edges is Five and Containing No Loops. IOP Conf. Series: Journal of Physics: Conf. Series 1338 (2019) 012043. doi:10.1088/1742-6596/1338/1/012043
Wamiliana, Amanto and Nagari G.T. (2016). Counting the Number of Disconnected Labeled Graphs of Order Five without Parallel Edges International Series on Interdisciplinary Sciences and Technology (INSIST) Vol 1 (1) p 1-6.
Authors
Ansori, M., Wamiliana, & Puri, F. C. (2021). Determining The Number of Connected Vertex Labeled Graphs of Order Seven without Loops by Observing The Patterns of Formula for Lower Order Graphs with Similar Property. Science and Technology Indonesia, 6(4), 328–336. https://doi.org/10.26554/sti.2021.6.4.328-336
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