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Eccentric distance sum dan adjacent eccentric distance sum index graf petersen diperumum

Zalicha, Rafenda Mundi Widya (2019) Eccentric distance sum dan adjacent eccentric distance sum index graf petersen diperumum. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA:

Eccentric distance sum dari didefinisikan sebagai ξ^ds (G)=∑_(v∈V(G))▒〖e(v)D(v)〗dan adjacent eccentric distance sum index dari didefinisikan sebagai ξ^sv (G)=∑_(v∈V(G))▒(e(v)D(v))/(deg⁡(v)), dengan e (v) eksentrisitas titik v adalah jarak terbesar antara titik v dan titik lainnya di G.D(v) menunjukkan jumlah semua panjang lintasan terpendek (jarak) dari titik v ke setiap titik yang lain pada graf D. Derajat titik v atau deg(v) merupakan jumlah sisi yang terkait langsung dengan v.

Graf Petersen diperumum dinotasikan GP(n,k) untuk bilangan positif n≥3 dan 1≤k≤(n-1)/2, adalah graf dengan himpunan titik V (GP(n,k))={u_0,u_1,…,u_(n-1),v_0,v_1,…,v_(n-1)} dan himpunan sisi E(GP(n,k))={u_i u_((i+1) ),v_i v_((i+k) ),u_i v_i |i=0,1,…,n-1}, dengan penambahan di dalam indeks (i+1),(i+k) adalah modulo n Dengan memperhatikan GP(n,k) adalah graf teratur-3. Penelitian ini bertujuan untuk mengetahui eccentric distance sum dan adjacent eccentric distance sum index graf Petersen diperumum yang kemudian menjadi teorema. Hasil penelitian ini adalah:

1.Eccentric distance sum dan Adjacent eccentric distance sum index graf Petersen diperumum GP(n,1) dengan n bilangan bulat positif dan n≥3,

2.Eccentric distance sum dan adjacent eccentric distance sum index graf Petersen diperumum GP(n,2) dengan n bilangan bulat positif dan n≥8 .

Untuk penelitian selanjutnya diharapkan dapat menemukan teorema terkait eccentric distance sum dan adjacent eccentric distance sum index graf Petersen diperumum GP(n,k) dengan k∉{1,2}.

ENGLISH:

Eccentric distance sum of is defined as ξ^ds (G)=∑_(v∈V(G))▒〖e(v)D(v)〗 and adjacent eccentric distance sum index of G is defined as ξ^ds (G)=∑_(v∈V(G))▒〖e(v)D(v)〗, with eccentricity e(v) of a vertex v is the largest distance between u and any other vertex v of G. denotes the sum of distances between v and all other vertices of G. The degree of a vertex v∈V(G) is denoted by deg(v) and is the number of vertices adjacent to v.

The generalized Petersen graph GP(n,k) for positive integers n≥3 and 1≤k≤(n-1)/2 , is defined to have vertex set V(GP(n,k))={u_0,u_1,…,u_(n-1),v_0,v_1,…,v_(n-1)} and edge set E(GP(n,k))={u_i u_((i+1) ),v_i v_((i+k) ),u_i v_i |i=0,1,…,n-1}, where addition in the subscripts is modulo n. Notice that GP(n,k) is a regular 3-graph. The purpose of this research is to find the formula of eccentric distance sum and adjacent eccentric distance sum index generalized Petersen graph . The result of this research are:

1.Eccentric distance sum and Adjacent eccentric distance sum index generalized Petersen graph GP(n,1), for positif integers n and n≥3,

2.Eccentric distance sum and adjacent eccentric distance sum index generalized Petersen graph GP(n,2) for positif integers n and n≥8.

For the further research the author suggest to determine the theorem related to the eccentric distance sum and adjacent eccentric distance sum index generalized Petersen graph GP(n,k) for k∉{1,2}.

Item Type: Thesis (Undergraduate)
Supervisor: Abdussakir, Abdussakir and Nashichuddin, Achmad
Contributors:
ContributionNameEmail
UNSPECIFIEDAbdussakir, AbdussakirUNSPECIFIED
UNSPECIFIEDNashichuddin, AchmadUNSPECIFIED
Keywords: eccentric distance sum; adjacent eccentric distance sum index; graf Petersen diperumum; eccentric distance sum; adjacent eccentric distance sum index; generalized Petersen Graph
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Heni Kurnia Ningsih
Date Deposited: 30 Apr 2020 13:15
Last Modified: 19 Sep 2020 15:18
URI: http://etheses.uin-malang.ac.id/id/eprint/15231

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