Wamiliana, Wamiliana and Amanto, Amanto and Usman, Mustofa and Muslim Ansori, Muslim and 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). pp. 131-135. ISSN e -ISSN:2580-4391 p -ISSN:2580-4405

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Official URL: http://sciencetechindonesia.com/index.php/jsti


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 that graph contains 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 find that the formula to count the number of connected vertices labeled graphs of order six with m edges that containing maximum ten loops and no parallel edges N (G(� )6,m) = ∑15 t=5 N (G(� )6,m,t ), where t ≤ m; and N (G(� )6,m,5) = 1296(m 5 ), N (G(� )6,m,6) = 1980 m−1 5 �, N (G(� )6,m,7) = 3330 m−2 5 �, N (G(� )6,m,8) = 4620 m−3 5 �, N (G(� )6,m,9= 6660 m−4 5 �, N (G(� )6,m,10) = 2640 m−5 5 �, N (G(� )6,m,11) = 1155 m−6 5 �, N (G(� )6,m,12) = 420 m−7 5 �, N (G(� )6,m,13) = 150 m−8 5 �N (G(� )6,m,14) = 15 m−9 5 �, N (G(� )6,m,15) = m−10 5 �

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Depositing User: WAMILIANA
Date Deposited: 16 Oct 2020 02:40
Last Modified: 16 Oct 2020 02:40
URI: http://repository.lppm.unila.ac.id/id/eprint/24313

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