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Muslim Ansori
Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandarlampung, 35145, Indonesi
Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Physics

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Enumerate the Number of Vertices Labeled Connected Graph of Order Seven Containing No Parallel Edges Muslim Ansori; Wamiliana; Fitriani; Yudi Antoni; Desiana Putri
Science and Technology Indonesia Vol. 7 No. 3 (2022): July
Publisher : Research Center of Inorganic Materials and Coordination Complexes, FMIPA Universitas Sriwijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (744.732 KB) | DOI: 10.26554/sti.2022.7.3.392-399

Abstract

A graph that is connected G(V,E) is a graph in which there is at least one path connecting every two vertices in G; otherwise, it is called a disconnected graph. Labels or values can be assigned to the vertices or edges of a graph. A vertex-labeled graph is one in which only the vertices are labeled, and an edges-labeled graph is one in which only edges are assigned values or labels. If both vertices and edges are labeled, the graph is referred to as total labeling. If given n vertices and m edges, numerous graphs can be made, either connected or disconnected. This study will be discussed the number of disconnected vertices labeled graphs of order seven containing no parallel edges and may contain loops. The results show that number of vertices labeled connected graph of order seven with no parallel edges is N(G7,m, g)l= 6,727×Cm6; while for 7≤g≤ 21, N(G7,m, g)l= kg C(m−(g−6))g−1, where k7 =30,160, k8 = 30,765, k9=21,000, k10 =28,364, k11= 26,880, k12=26,460 , k13 = 20,790, k14 =10,290, k15 = 8,022, k16 = 2,940, k17 =4,417, k18 = 2,835, k19 =210, k20 = 21, k21= 1.
Co-Authors . Wamiliana Desiana Putri Fitriani Yudi Antoni