Dimensi Metrik Monofonik Lokal Sentral Graf

Lathifah, Ririana Annisatul (2025) Dimensi Metrik Monofonik Lokal Sentral Graf. Masters thesis, Institut Teknologi Sepuluh Nopember.

Text 6002231003 - Master_Thesis.pdf - Accepted Version Restricted to Repository staff only until 1 April 2027. Download (7MB) | Request a copy

Abstract

Diberikan graf terhubung sederhana G, dengan V(G) merepresentasikan himpunan seluruh simpul pada G, dan E(G) merepresentasikan himpunan seluruh sisi pada G. Jika u,v elemen V(G), maka jarak monofonik dari u ke v adalah panjang lintasan terpanjang dari u ke v yang tidak memiliki tali busur, yaitu sisi yang menghubungkan dua simpul yang tidak bertetangga pada suatu lintasan, dan dilambangkan dengan d_m(u,v). Himpunan W subset V(G) disebut himpunan pembeda monofonik lokal jika setiap dua simpul yang bertetangga pada G memiliki representasi monofonik yang berbeda terhadap himpunan W. Himpunan S subset V(G) disebut himpunan sentral monofonik jika untuk setiap simpul v di S, eksentrisitas monofonik dari v sama dengan radius monofonik dari graf G. Himpunan P subset V(G) disebut himpunan pembeda monofonik lokal sentral jika P merupakan himpunan pembeda monofonik lokal, dan S subset P. Pada penelitian ini, diselidiki pola himpunan sentral monofonik dan nilai dimensi metrik monofonik lokal sentral dari beberapa graf khusus yaitu graf lintasan, graf siklus, graf lengkap , graf bintang dan graf bipartit lengkap, graf hasil operasi degree splitting dari graf tersebut, serta graf hasil operasi join antara graf tersebut dengan K_1 dan K_2. Pada graf G berordo n, nilai dimensi metrik monofonik lokal sentral dari G adalah n jika dan hanya jika eksentrisitas monofonik seluruh simpul v pada G bernilai sama.
==================================================================================================================================
Given a simple connected graph G, and let V(G) represent the set of all vertices in G, and E(G) represent the set of all edges in G. For u, v elements in V(G), the monophonic distance from u to v is defined as the length of the longest path from u to v that does not contain a chord, where a chord is an edge connecting two non-adjacent vertices on a path. The monophonic distance is denoted by d_m(u,v). A subset W of V(G) is called a local monophonic resolving set if every pair of adjacent vertices in G has a different monophonic representation with respect to W. A subset S of V(G) is called a monophonic central set if, for every v in S, the monophonic eccentricity of v equals to the monophonic radius of G. A subset P of V(G) is called a local central monophonic resolving set if P is a local monophonic resolving set and S is subset of P.This study investigates the patterns of the monophonic central set and the values of local central monophonic metric dimensions for several special graphs, including path graphs, cycle graphs, complete graphs, star graphs, and complete bipartite graphs. Additionally, it analyzes the degree-splitting operation on these graphs and the join operation between these graphs with K_1 and K_2. For a graph G with order n, the local central monophonic metric dimension of G is n if and only if the monophonic eccentricities of all vertices v in V(G) are same.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	dimensi metrik monofonik, himpunan pembeda lokal sentral, himpunan sentral monofonik, operasi join, operasi degree splitting. monophonic metric dimension, central local resolving set, monophonic central set, joint operation, degree splitting operation.
Subjects:	Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA166 Graph theory
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Mathematics > 44101-(S2) Master Thesis
Depositing User:	Ririana Annisatul Lathifah
Date Deposited:	03 Feb 2025 04:08
Last Modified:	03 Feb 2025 04:08
URI:	http://repository.its.ac.id/id/eprint/117519

Actions (login required)

View Item