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Jumlah jarak eksentrik pada Graf lily

Tamam, Moh. Badrut (2020) Jumlah jarak eksentrik pada Graf lily. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

ABSTRAK

Graf lily Ly(m,n) adalah graf dengan himpunan titik V(Ly(m,n))={v_(i,j),v_c }(i=0,1,…,n; j=0,1,…,m-1) dan himpunan sisi E(Ly(m,n))={v_(0,j) v_c }(j=0,1,…,m-1;i=0,1,…,n) ∪ {v_(i,j) v_(i+1,j),v_(i,j) v_(i+1,j+1(mod m) ),(j=0,1,…,m-1)} dengan n≥1 dan m≥2. Misal G adalah graf terhubung, jumlah jarak eksentrik dari graf G didefinisikan ξ^ds (G)=∑_(u∈V(G))▒〖e(u)D(u)〗, e(u) merupakan eksentrisitas titik u di G dan D(u) merupakan jumlah titik u di G.

Tujuan dari penelitian ini adalah memperoleh pola jumlah jarak eksentrik pada graf lily Ly(m,1) yang nantinya dijadikan teorema. Jumlah jarak eksentrik pada Ly(m,1) adalah ξ^ds (Ly(m,1))={█(2m(5m+4),m=2 @3m(12m-13),m=3@m(43m-49),m≥4 )┤ ,m∈N
Bagi penelitian selanjutnya diharapkan menemukan pola jumlah jarak eksentrik pada graf lily Ly(m,n) dengan n≠1.

ABSTRACT

Lily graph Ly(m,n)is a graph with the set of vertices V(Ly(m,n))={v_(i,j),v_c }(i=0,1,…,n; j=0,1,…,m-1)and set of edges E(Ly(m,n))={v_(0,j) v_c }(j=0,1,…,m-1;i=0,1,…,n) ∪ {v_(i,j) v_(i+1,j),v_(i,j) v_(i+1,j+1(mod m) ),(j=0,1,…,m-1)} where n≥1 and m≥2. Let G be a connected graph, the eccentric-distance sum of G is defined as ξ^ds (G)=∑_(u∈V(G))▒〖e(u)D(u)〗, where e(u)is the eccentricity of vertex in u di G and D(u)is distance sum of vertex u in G.

The purpose of this research is to find a formula of eccentric-distance sum
of lily graph Ly(m,1) which will be stated as theorem. The eccentric-distance
sum of Ly(m,1)is ξ^ds (Ly(m,1))={█(2m(5m+4),m=2 @3m(12m-13),m=3@m(43m-49),m≥4 )┤ ,m∈N For further research, it is sugested to find the formula of eccentric-distance sum of lily graph Ly(m,n)and n≠1.

Item Type: Thesis (Undergraduate)
Supervisor: Abdussakir, Abdussakir and Jauhari, Mohammad Nafie
Contributors:
ContributionNameEmail
UNSPECIFIEDAbdussakir, AbdussakirUNSPECIFIED
UNSPECIFIEDJauhari, M. NafieUNSPECIFIED
Keywords: Jumlah jarak eksentrik; Graf lily; eccentric-distance sum; lily graph
Subjects: 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010101 Algebra and Number Theory
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Mohammad Badrut Tamam
Date Deposited: 30 Jun 2021 10:34
Last Modified: 20 Jun 2023 11:30
URI: http://etheses.uin-malang.ac.id/id/eprint/24606

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