Dimensi Detour Nonlokal pada Graf Dasar dan Beberapa Graf Korona

Syarifudin, Muhammad Fikri (2026) Dimensi Detour Nonlokal pada Graf Dasar dan Beberapa Graf Korona. Other thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diberikan graf terhubung G = (V(G),E(G) dengan himpunan simpul V(G) dan himpunan sisi E(G), himpunan terurut S = {s1,s2,s3,...,sk} dengan S ⊆ V(G), dan v ∈ V(G). Representasi rD(v|S) dari v terhadap S adalah k-vektor (D(v,s1),D(v,s2),D(v,s3),...,D(v,sk)) dengan D(v,si),i ∈ {1,2,3,...,k} adalah detour dari v ke si. Himpunan S disebut himpunan pembeda detour dari G jika rD(v|S) ̸ = rD(u|S), untuk setiap u,v ∈ V (G). Himpunan pembeda detour minimal dari G disebut basis detour dari G dan kardinalitasnya disebut dimensi detour dari G, dinotasikan dengan Ddim(G). Setiap u dan v yang tidak bertetangga berlaku rD(u|S) ̸ = rD(v|S) maka himpunan pembeda detour S disebut himpunan pembeda detour nonlokal dari G dan kardinalitas minimalnya disebut dimensi detour nonlokal dari G dan dinotasikan dengan Ddimnl(G). Pada penelitian tugas akhir ini ditentukan nilai dimensi detour nonlokal dari graf dasar dan beberapa graf varian korona. =======================================================================================================================================
Given a connected graph G = (V(G),E(G) with vertex set V(G) and edge set E(G), an ordered set S = {s1,s2,s3,...,sk} with S ⊆ V (G), and v ∈ V(G). The representation rD(v|S) of v with respect to S is a k-vector (D(v,s1),D(v,s2),D(v,s3),...,D(v,sk)) where D(v,si),i ∈ {1,2,3,...,k} is the detour from v to si. The set S is called detour resolving set of G if rD(v|S) ̸ = rD(u|S), for every u,v ∈ V (G). The set of minimal detour resolving set of G is called the detour basis of G and its cardinality is called the detour dimension of G, denoted by Ddim(G). Every non-adjacent u and v rD(u|S) ̸ = rD(v|S) then the detour resolving set S is called the nonlocal detour resolving set of G and its minimal cardinality is called the nonlocal detour dimension of G and is denoted by Ddimnl(G). This study investigates and establishes the nonlocal detour dimension of base graphs alongside selected corona variant graphs.

Item Type:	Thesis (Other)
Uncontrolled Keywords:	Detour, Himpunan Pembeda Detour, Dimensi Detour Nonlokal, Operasi Korona, Detour, Detour Resolving Set, Nonlocal Detour Dimension , Corona Operation
Subjects:	Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA166 Graph theory
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44201-(S1) Undergraduate Thesis
Depositing User:	Muhammad Fikri Syarifudin
Date Deposited:	04 Aug 2026 07:24
Last Modified:	04 Aug 2026 07:24
URI:	http://repository.its.ac.id/id/eprint/143504

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