Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک ایرانیان IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 7 14 8888 13 en jalali 1397 7 1 gregorian 2018 10 1 13 2 online 1 fulltext
en Vector Space semi-Cayley Graphs عمومى General پژوهشي Research paper <p>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')\$.</p> Cayley graph, Vector space, Basis 83 91 http://ijmsi.ir/browse.php?a_code=A-10-1774-1&slc_lang=en&sid=1 B. Tolue b.tolue@gmail.com `10031947532846005260` 10031947532846005260 Yes Department of Mathematics,Hakim Sabzevari University