### Sifat-Sifat Matriks Ketetanggaan Pada Graf Petersen

Yuco Alsbaldo - Universitas Negeri Padang

#### Abstract

Graphs are  used to represent discrete  objects and the relationships between these objects. One of the best known and very popular examples of graphs is Petersen graph.Petersen graph is very popular  because  of  its  uniqueness  as  a counterexample in  many  places  and  has  many  interesting properties.  Graphs  can  beexpressed  in  the  form  of  a  matrix adjacencywhich  is  denoted.  When  a graph can be  expressed in  the form of an adjacency  matrix, its determinants and eigenvalues can be determined. This research is a theoretical research through literature study. The purpose of this study is to find out how the properties of the adjacency matrix on a Petersen graph are. The concept that will be  discussed  in  this  research  is  how  the  properties  of  the  determinants  and  eigenvalues of  the adjacency  matrix  on  the  Petersen  graph. The  result  of  the  research  is  that  the  determinant  of  the adjacency  matrix  on  the  Petersen  graph  is  positive  with  three  different  eigenvalues and  can  be diagonalized because the algebraic multiplicity is the same as the geometric multiplicity mA = mG

PDF

#### References

Ginting, Juneidi. 2016. Graf Petersen dengan Beberapa Sifat-Sifat yang Berkaitan dalam Teori Graph. No 1 Vol 2. Medan: Universitas Negeri Medan.

Holton D.A. and J. Sheehan. 1993. The Petersen Graph. Cambridge: University Press.

Rores. Anton. 2004. Aljabar Linear Elementer Versi Aplikasi: Edisi 8 Jilid 1. Jakarta: Erlangga.

Bapat, R. 2014. Graphs and Matrices Second Edition. Hindustan Book Agency: New Delhi.

Alireza, abdollahi. 2012. Determinants of Adjacency Matrices of Graphs. Vol. 1 No. 4, 9-16.University of Isfahan: Department of Mathematics.

Farrugia, Alexander dkk. 2013. On the Inverse of the Adjacency Matrix of a Graph.University of Malta: Department of Mathematics.

DOI: http://dx.doi.org/10.24036/unpjomath.v6i3.11910