Main Article Content

Wamiliana Wamiliana Amanto Amanto Mustofa Usman Muslim Ansori Fadila Cahya Puri
DOI: Published Oct 9, 2020


A Graph G (V, E) is said to be a connected graph if for every two vertices on the graph there exist at least a path connecting them, otherwise, the graph is disconnected. Two edges or more that connect the same pair of vertices are called parallel edges, and an edge that starts and ends at the same vertex is called a loop.  A graph is called simple if it containing no loops nor parallel edges. Given n vertices and m edges, m ≥ 1, there are many graphs that can be formed, either connected or disconnected. In this research, we will discuss how to calculate the number of connected vertices labeled graphs of order six (isomorphism graphs are counted as one), with a maximum loop of ten without parallel edges.


Abstract 152 times PDF 93 times

Article Details

How to Cite
WAMILIANA, Wamiliana et al. Enumerating the Number of Connected Vertices Labeled Graph of Order Six with Maximum Ten Loops and Containing No Parallel Edges. Science and Technology Indonesia, [S.l.], v. 5, n. 4, p. 131-135, oct. 2020. ISSN 2580-4391. Available at: <>. Date accessed: 27 jan. 2021. doi:


Agnarsson, G. and Greenlaw, R. D. (2007). Graph Theory Modelling Application and Algorithms. Pearson/Prentice Education, Inc., New Jersey.

Amanto, Efendi M.F N, and Wamiliana. Penentuan Banyaknya Graf Tak Terhubung Berlabel Titik Berorde Lima Tanpa Loop dengan Banyaknya
Garis 3-Paralel adalah Enam. (In Indonesian), Prosiding Konferensi Nasional Matematika XIX, Malang, pp. 169-176.

Al Etaiwi W. M. Encryption Algorithm Using Graph Theory. Journal of Scientific Research and
Reports 3 (19): 2519-2527.

Brandes U., and Cornelsen S. (2009). Phylogenetic graph models beyond trees. Discrete Applied
Mathematics. Vo; 157 (10), pp. 2361-2369.

Bóna, Miklós. (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.

Deka D. K.(2015). Application of Graph Theory in Phylogenetics: The Primate Approach. Asia
Pacific Mathematics Newsletter. Vol. 5 (2), pp. 16-20.

Harary F., and Palmer, E. M. (1973). Graphical Enumeration. Academic Press, New York.

Hsu L. H., and Lin C.K. (2009). Graph Theory and Interconnection Network. Taylor and Francis Group, LLC, New York.

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), pp. 263-271.doi: 10.1016/j.ejbas.2016.07.004

Priyadarsini, P.L.K. (2015). A Survey on some Applications of Graph Theory in Cryptography.
Journal of Mathematical Sciences and Cryptography. Vol. 18 (3), pp. 209 – 217.

Stanley, R.P. (1997). Enumerative Combinatorics, 1, no. 49 of Cambridge Studies in Advanced
Mathematics. Cambridge University Press, New York. 1997

Stanley, R.P. (1999). Enumerative Combinatorics, 2 no. 62 of Cambridge Studies in Advanced
Mathematics. Cambridge University Press, New York, 1999.

Vasudev C. Graph Theory with Application. (2006). New Age International Limited.
Wamiliana, Amanto, and G. T. Nagari. (2016). Counting the Number of Disconnected labeled Graphs of Order Five Without Parallel Edges.
International Series on Interdisciplinary Science and Technology (INSIST), 1, no. 1, p. 1 – 6, 2016.

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

Wilf, H, 1. Generating Functionology. (1994). Academic Press, second Edition, New York.