Volume 13, Issue 2 (10-2018)                   IJMSI 2018, 13(2): 83-91 | Back to browse issues page

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Tolue B. Vector Space semi-Cayley Graphs. IJMSI. 2018; 13 (2) :83-91
URL: http://ijmsi.ir/article-1-817-en.html
Abstract:

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph \${rm Cay(mathcal{V},S)}\$ is a graph with the vertex set the whole vectors of the vector space \$mathcal{V}\$ and two vectors \$v_1,v_2\$ join by an edge whenever \$v_1-v_2in S\$ or \$-S\$, where \$S\$ is a basis of \$mathcal{V}\$. This fact causes a new connection between vector spaces and graphs. The vector space Cayley graph is made of copies of the cycles of length \$t\$, where \$t\$ is the cardinal number of the field that \$mathcal{V}\$ is constructed over it. The vector space Cayley graph is generalized to the graph \$Gamma(mathcal{V},S)\$. It is a graph with vertex set whole vectors of \$mathcal{V}\$ and two vertices \$v\$ and \$w\$ are adjacent whenever \$c_{1}upsilon+ c_{2}omega = sum^{n}_{i=1} alpha_{i}\$, where \$S={alpha_1,cdots,alpha_n}\$ is an ordered basis for \$mathcal{V}\$ and \$c_1,c_2\$ belong to the field that the vector space \$mathcal{V}\$ is made of over. It is deduced that if \$ S'\$ is another basis for \$mathcal{V}\$ which is constructed by special invertible matrix \$P\$, then \$Gamma(mathcal{V},S)cong Gamma(mathcal{V},S')\$.

Type of Study: Research paper | Subject: General