Some Properties of Derived Graph Algebra

Let <(A(G))under bar> = (V boolean OR {infinity} ; f(A), infinity) be graph algebra corresponding to a graph G where f(A) is a binary operation. Then sigma<([A(G)])under bar> = (V boolean OR {infinity}; sigma (f)(A), infinity) is called a derived graph algebra, where sigma is a regular hypersubstitution. The set of all term equations s approximate to t which G satisfies(sigma) s approximate to t is denoted by Id(sigma)({G}). The class of all derived graph algebras satisfy for all term equations in Id(sigma)({G}) is called the derived graph variety generated by {G} on sigma denoted by nu(sigma)({G}). A term equation s approximate to t is called a derived identity in nu(sigma)({G}) if sigma<([A(G')])under bar> satisfies s approximate to t for all sigma<([A(G')])under bar> is an element of nu(sigma)({G}). In this paper we would like to consider some properties and some relation between derived graph algebra and graph algebra.