Vector Space Semi-Cayley Graphs

The vector space Cayley graph Cay(V; S) is a graph with the vertex set the whole vectors of the vector space V and two vectors v1; v2 join by an edge whenever v1 􀀀 v2 2 S or 􀀀S, where S is a basis of V. The vector space Cayley graph contains copies of the n-gons, where n is the cardinal number of the eld that V is constructed over it. 􀀀(V; S) is another graph with vertex set V, which is dened in this paper. It is a graph whose vertices v and w are adjacent whenever c1+c2! = Pn i=1 i,where v;w 2 V, S = f1; ; ng is an ordered basis for V and c1; c2 belong to the eld that the vector space V is made of over. It is deduced that if S0 is another basis for V which is constructed by special invertible matrix P, then 􀀀(V; S) = 􀀀(V; S0).