AU - Tolue, B.
TI - Vector Space semi-Cayley Graphs
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 13
VI - 2
IP - 2
4099 - http://ijmsi.ir/article-1-817-en.html
4100 - http://ijmsi.ir/article-1-817-en.pdf
SO - IJMSI 2
ABĀ - 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 $Gamma(mathcal{V},S)cong Gamma(mathcal{V},S')$.
CP - IRAN
IN - Department of Mathematics, Hakim Sabzevari University, Sabzevar, Iran
LG - eng
PB - IJMSI
PG - 83
PT - Research paper
YR - 2018