Some Algebraic Properties of a Class of Integral Graphs Determined by Their Spectrum

Let Γ = V , E be a graph. If all the eigenvalues of adjacency matrix graph id="M2"> are integers, then we say that id="M3"> is an integral A id="M4"> determined by its spectrum if every cospectral to it in fact isomorphic it. In this paper, investigate some algebraic properties Cayley id="M5"> Cay ℤ n S , where id="M6"> p m ( id="M7"> prime integer and id="M8"> ∈ mathvariant="normal">ℕ ) id="M9"> open="{" close="}" a | 1 . First, show id="M10"> Also, determine automorphism group id="M11"> Moreover, id="M12"> id="M13"> K v mathvariant="normal">▽ their spectrum.