Applications of linear transformations

In this paper, we applied linear transformations in the graph theory. Firstly, we constructed vector spaces of a finite number of elements over the field F={0,1}.Then we used them to construct linear transformations (in fact linear operators), defined on each of the vector spaces of the degrees of the vertices;〖(D〗_V,+_V,._V); the vector space of the vertices;(V,⨁▒〖,⨀)〗 ; and the vector space of the number of the paths between the vertex a and the other vertices;〖(P〗_a,+_P,._P);.The last linear transformations is defined from V into D_V.