Spectrum Adjacency, spectrum Detour dan spectrum Laplace pada graf Türan

Faizah, Nurul (2012) Spectrum Adjacency, spectrum Detour dan spectrum Laplace pada graf Türan. Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA :

Teori graf lahir pada tahun 1736 melalui tulisan L. Euler, seorang matematikawan Swiss, yang berisi tentang upaya pemecahan masalah jembatan Konigsberg yang sangat terkenal di Eropa. Dalam penelitian ini teori graf akan di representasikan ke dalam bentuk aljabar yaitu berupa matriks. Dan diolah dengan menggunakan metode aljabar.

Matriks Adjacency dari graf (G) ditulis A(G) adalah matriks yang unsur a_ij=0 jika v_i v_j∈E(G) dan a_ij=0 jika v_i v_j∈E(G). Matriks diagonal dari graf (G), ditulis D(G) adalah matriks yang unsur a_ij=0 jika i≠j dan a_ij=deg(v_1) jika i=j. Matriks Detour dari graf (G), ditulis DD(G) adalah matriks dengan unsur a_ij merupakan jarak lintasan terpanjang dari v_i ke v_j. Matriks Laplace dari graf (G) adalah L(G)=D(G)-A(D). Spectrum dari matriks A (G), DD(G) dan L(G) masing-masing disebut Spectrum Adjacency, Spectrum Detour dan Spectrum Laplace. Pada penelitian ini, ditentukan pola Spectrum Adjacency, Spectrum Detour dan Spectrum Laplace dari graf T ran. Hasil penelitian ini, dinyatakan dalam teorema berikut:

1. Spectrum Adjacency dari graf T_(k,kn) adalah
Spec (T_(k,kn)= [(-n&0&(k-1)n@(k-1)&k(n-1)&1)]

2. Spectrum Detour dari graf T_(k,kn) adalah
〖Spec〗_DD (T_(k,kn)= [(-(kn-1)&〖(kn-1)〗^2@(kn-1)&1)]

3. Spectrum Laplace dari graf T_(k,kn) adalah
〖Spec〗_L (T_(k,kn)= [(0&(k-1)n&kn@1&k(n-1)&(k-1) )]

ENGLISH :

Graph theory was born in 1736 in writing L. Euler, a Swiss mathematician, which contains about Konigsberg bridge problem-solving efforts are very well known in Europe. In this graph theory whose team will be represented in the form of a matrix algebra. And processed using algebraic methods.

Adjacency matrix of the graph (G) is written by A(G) is the matrix with element a_ij=0 if v_i v_j∈E(G) and a_ij=0 if v_i v_j∈E(G). Diagonal matrix of the graph (G), written by D(G) is the matrix element a_ij=0 if i≠j and a_ij=deg(v_1) if i=j. Detour matrix of the graph (G), written by DD(G) is a matrix with elements a_ij is the longest track distance from v_i to v_j. Laplace matrix of the graph (G) is L(G)=D(G)-A(D) Spectrum of the matrix A(G), DD(G) and L(G) are called Adjacency Spectrum, Spectrum Detour and Spectrum Laplace. In this study, determined the pattern Adjacency Spectrum, Spectrum Detour and Spectrum Laplace of T ran graph. The results of this study, stated in the following theorem:

1. Spectrum Adjacency of graph is
Spec (T_(k,kn)= [(-n&0&(k-1)n@(k-1)&k(n-1)&1)]

2. Spectrum Detour of graph is
〖Spec〗_DD (T_(k,kn)= [(-(kn-1)&〖(kn-1)〗^2@(kn-1)&1)]

3. Spectrum Laplace of the graph is
〖Spec〗_L (T_(k,kn)= [(0&(k-1)n&kn@1&k(n-1)&(k-1) )]

Item Type: Thesis (Undergraduate)
Supervisor: Abdussakir, Abdussakir and Nashichuddin, Achmad
Keywords: spectrum adjacency; spectrum detour; specrtum laplace; T ran graph; spectrum adjacency; spectrum detour; specrtum laplace; graf T ran
Subjects: 01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010101 Algebra and Number Theory
01 MATHEMATICAL SCIENCES > 0101 Pure Mathematics > 010199 Pure Mathematics not elsewhere classified
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: M. Muzakir
Date Deposited: 23 May 2017 08:18
Last Modified: 23 May 2017 08:18
URI: http://etheses.uin-malang.ac.id/id/eprint/6814

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