et V be a finite dimensional vector space on a field F . The suace inclusion graph, In(V), on V is a graph whose vertices is the collection of all nontrivial proper suaces of V and to vertices are adjacent if one is contained in other. In this thesis study basic properties and parameters of In(V). It is shown that In(V) and In(W) are isomorphic if and only if V and W are isomorphic. Some properties of suace inclusion graph are studied when the base field is finite. Also we introduce the nonzero component graph, ??(V), ofVoverFwith respect to a given basis A ={?_? و?_? و…و?_n } of V. The vertices of this graph are nonzero vectors of V and two vertices a and b are adjacent if the coefficient of at least one of ?_i و i?{?و ?و…و n} in the basic representations of a and b with respect to A is nonzero. We show that ?(V) is connected and determine its domination number and independence number. We also study the inter-relationship between vector space isomorphisms and graph isomorphisms, and it is shown that two graph are isomorphic if and only if the corresponding vector spaces are so. Finally, we determine the degree of each vertices in case the base field is finite.