Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
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8888
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jalali
1397
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gregorian
2018
10
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online
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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
`10031947532846006513`

10031947532846006513
Yes
Department of Mathematics,Hakim Sabzevari University