Dimensi Detour Lokal pada Graf

Wananda, Fiqhi Setya Wananda (2025) Dimensi Detour Lokal pada Graf. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diberikan graf terhubung G=(V(G),E(G)) berordo n, dengan himpunan simpul V(G)={v_1,v_2,...,v_|V(G)|} dan himpunan sisi E(G)={e_1,e_2,...,e_|E(G)|}. Representasi detour dari v∈V(G) terhadap himpunan terurut W, r_D(v|W) adalah k-vektor r_D(v|W)=(D(v,w_1),D(v,w_2),...D(v,w_k)), dengan D(u,v) adalah jarak terpanjang antar simpul u dan v pada graf G. Himpunan terurut W adalah himpunan pembeda detour untuk graf G jika representasi detour dari simpul u dan v berbeda, yaitu r_D(u|W)≠r_D(v|W), untuk setiap u,v∈V(G). Himpunan pembeda detour dengan banyak elemen minimal disebut dengan basis detour. Kardinalitas basis detour untuk graf G disebut dimensi detour dari G, dinotasikan dengan Ddim(G). Himpunan terurut W disebut dengan himpunan pembeda detour lokal untuk graf G jika representasi detour dari simpul u dan v berbeda, yaitu r_D(u|W)≠r_D(v|W), untuk setiap u,v∈V(G), dan u~v. Himpunan pembeda detour lokal dengan banyak elemen minimal disebut dengan basis detour lokal. Kardinalitas basis detour lokal dari G disebut dimensi detour lokal dari G, dinotasikan Ddim_l(G). Pada tugas akhir ini, dibahas dan ditentukan dimensi detour lokal pada graf P_n,C_n,S_n,K_n,K_(r,s),C_n⊙K_1,C_n◊K_1,C_n⊛K_1,C_n⊙_degK_1.
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Given a connected graph G=(V(G),E(G)) of order n, with wertex set V(G)={v_1,v_2,...,v_|V(G)|} and edge set E(G)={e_1,e_2,...,e_|E(G)|}. The detour representation of v∈V(G) with respect to the ordered set W, r_D(v|W) is a k-vector r_D(v|W)=(D(v,w_1),D(v,w_2),...D(v,w_k)), where D(u,v) is the longest distance between vertices u and v in graph G. The ordered set W is a detour resolving set for graph G if the detour representations of vertices u and v are distinct, i.e., r_D(u|W)≠r_D(v|W), for every u,v∈V(G). detour resolving set with minimum cardinality is called a detour basis. The cardinality of a detour basis for graph G is called the detour dimension of G, denoted by Ddim(G). The ordered set he ordered set W is called a local detour resolving set for graph G if the detour representations of vertices u and v are distinct, i.e., r_D(u|W)≠r_D(v|W), for every u,v∈V(G), and u~v. A local detour resolving set with minimum cardinality is called a local detour basis. The cardinality of a local detour basis of G is called the local detour dimension of G, denoted by Ddim_l(G). n this final project, the local detour dimension is discussed and determined for P_n,C_n,S_n,K_n,K_(r,s),C_n⊙K_1,C_n◊K_1,C_n⊛K_1,C_n⊙_degK_1.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Dimensi metrik, Dimensi detour, Dimensi metrik lokal, Metric dimension, Detour dimension, Local metric dimension
Subjects:	Q Science > QA Mathematics > QA166 Graph theory
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Fiqhi Setya Wananda
Date Deposited:	04 Aug 2025 12:32
Last Modified:	04 Aug 2025 12:32
URI:	http://repository.its.ac.id/id/eprint/124572

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