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) | |||||||||
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Supervisor: | Abdussakir, Abdussakir and Nashichuddin, Achmad | |||||||||
Contributors: |
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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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