We consider the adjacency graphs of the linear feedback shift registers (LFSRs) with characteristic polynomials of the form l(x)p(x), where l(x) is a polynomial of small degree and p(x) is a primitive polynomial. It is shown that, their adjacency graphs are closely related to the association graph of l(x) and the cyclotomic numbers over finite fields. By using this connection, we give a unified...

Graph algorithms that test adjacencies are usually implemented with an adjacency-matrix representation because the adjacency takes constant time matrices, but it linear in degree of vertices lists. In this article, we review adjacency-map representation, which supports tests expected time, and show graph run faster maps than lists by a small factor if they do not one or two orders magnitude per...

We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and topological properties e.g. homology groups. Other applications include visualization and path planning. Our algorithm determines cell adjacency information using...