Isospectral flows preserving some centrosymmetric structures Original Research Article

Let image be a simple undirected graph (no loops, no multiple edges) on n vertices. Let image be the set of real symmetric matrices of order n. A matrix image is said to be a matrix on image if ai,j=0 whenever i≠j and the vertices i, j of image are not joined by an edge of image. We recall that if F is a skew-symmetric operator on image, then the solution A(t) ofimagemaintains the spectrum of A0. The matrix image is said to be centrosymmetric if JAJ = A, where J is the matrix with ones on the secondary diagonal and zeros elsewhere. Centrosymmetric matrices are symmetric about the secondary diagonal. Centrosymmetric matrices appear in fields such as finite element analysis. We construct an isospectral flow on a graph image, with the property that if A0 is centrosymmetric, so is A(t), and discuss the limit of A(t) as t→∞