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Let G be a non-abelian group and Z(G) be the center of G. Associate a graph ΓG (called noncommuting graph of G) with G as follows: Take G{set minus}Z(G) as the vertices of ΓG, and join two distinct vertices x and y, whenever xy ≠ yx. Here, we prove that "the commutativity pattern of a finite non-abelian p-group determine its order among the class of groups"; this means that if P is a finite non-abelian p-group such that ΓP ≅ ΓH for some group H, then {pipe}P{pipe} = {pipe}H{pipe}  

This paper presents a new reduced-order modeling approach based on boundary element method. In this approach the eigenvalue problem of the unsteady flows is defined based on the unknown wake singularities. By constructing this reduced-order model, the body quasi-static eigenmodes are removed from the eigensystem and it is possible to obtain satisfactory results without static correction technique when enough eigenmodes are used. In addition to the conventional method, Eigenanalysis and reduced-order modeling of unsteady flows over a NACA 0012 airfoil and a wing with NACA 0012 section are performed using this new ROM method. Numerical examples are presented that demonstrate the accuracy and...