Rank Matriks Adjacency dari Graf Ln×Pm

Edit
Abstract: Graphs and matrices have many important roles in everyday life. That's why a lot of research has been done on the graph, one of which is about the rank of its adjacency matrix. During recent years numerous studies have been done regarding the rank of the adjacency matrix from the cross product of wo special graphs. The adjacency matrix 𝐴=�π‘Žπ‘–π‘—�𝑛×𝑛of a graph 𝐺 with 𝑛 vertices, is a matrix in which π‘Žπ‘–π‘— =1 if vertex 𝑣𝑖is adjacent to 𝑣𝑗in 𝐺 and π‘Žπ‘–π‘— =0, otherwise, where 𝑣𝑖and 𝑣𝑗are vertices of  𝐺. While rank is the number of rows or columns of the matrix which are linearly independent.
The purpose of this final project is to determine the relationship between the rank of adjacency matrix from 𝐿𝑛×π‘ƒπ‘š graph and the one from ladder graph 𝐿𝑛 and path π‘ƒπ‘š respectively. Before determining the general form of adjacency matrix from𝐿𝑛×π‘ƒπ‘š graph, first we determine the general form of the adjacency matrix from ladder graph 𝐿𝑛. Then, to determine the rank of the adjacency matrix from ladder graph 𝐿𝑛 and 𝐿𝑛×π‘ƒπ‘š graph we use M-file MATLAB program. The results of the program is then analyzed according to the concepts of algebra. From the analysis we obtain the formula of the rank of adjacency matrix from ladder graph 𝐿𝑛 is 2𝑛−1 for 𝑛=3π‘˜−1 and 2𝑛 for 𝑛≠3π‘˜−1 where π‘˜∈β„•. While, from the analysis of the rank of adjacency matrix from 𝐿𝑛×π‘ƒπ‘š graph, it can’t be found the regularity of the pattern of rank according to 𝑛 and π‘š.
Kata Kunci: Ladder Graph, Adjacency Matrix, Rank
Penulis: Novita Adelia, Nenik Estuningsih & Yayuk Wahyuni
Kode Jurnal: jpmatematikadd130071

Artikel Terkait :