Science and Technology Indonesia
Vol. 7 No. 3 (2022): July

Enumerate the Number of Vertices Labeled Connected Graph of Order Seven Containing No Parallel Edges

Muslim Ansori (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandarlampung, 35145, Indonesi)
Wamiliana (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandarlampung, 35145, Indonesia)
Fitriani (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandarlampung, 35145, Indonesi)
Yudi Antoni (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandarlampung, 35145, Indonesi)
Desiana Putri (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Lampung, Bandarlampung, 35145, Indonesi)



Article Info

Publish Date
28 Jul 2022

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.

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Journal Info

Abbrev

JSTI

Publisher

Subject

Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Environmental Science Materials Science & Nanotechnology Physics

Description

An international Peer-review journal in the field of science and technology published by The Indonesian Science and Technology Society. Science and Technology Indonesia is a member of Crossref with DOI prefix number: 10.26554/sti. Science and Technology Indonesia publishes quarterly (January, April, ...