This article concerns the system identification of a class of large scale systems called “circulant systems”. Circulant systems have a special property that allows them to be decomposed into simpler subsystems through a state transformation. This property has been used in literature for control design, and here we show how it can be used for system identification. The approach that is proposed ...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...

Semi-directed 2-circulant graph is a subgraph of an (undirected) 2-circulant graph in which the links of one type (i.e., short or long) are directed while the other links are undirected. The shortest paths in semi-directed circulant graphs are called the restricted shortest paths in 2-circulant graphs. In this paper we show that the problem of finding the restricted shortest paths is equivalent...

It is known that there exists a Minimum Distance Diagram (MDD) for circulant digraphs of degree two (or double-loop computer networks) which is an L-shape. Its description provides the diameter and the average distance of the graph on constant time. In this paper we clarify, justify and extend these diagrams to circulant digraphs of arbitrary degree by presenting monomial ideals as a natural to...

It has long been known that the number of spanning trees in circulant graphs with fixed jumps and n nodes satisfies a recurrence relation in n. The proof of this fact was algebraic (relating the products of eigenvalues of the graphs’ adjacency matrices) and not combinatorial. In this paper we derive a straightforward combinatorial proof of this fact. Instead of trying to decompose a large circu...

We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case. We present a direct product construction yielding improved bounds for small diameters and introduce a new general technique for “stitching” together circula...

The numerical solution of large and sparse nonsymmetric linear systems of algebraic equations is usually the most time consuming part of time-step integrators for differential equations based on implicit formulas. Preconditioned Krylov subspace methods using Strang block circulant preconditioners have been employed to solve such linear systems. However, it has been observed that these block cir...

Toeplitz systems can be solved efficiently by using iterative methods such as the conjugate gradient algorithm. If a suitable preconditioner is used, the overall cost of the method is O(n logn) arithmetic operations. Circulant matrices are frequently employed for the preconditioning of Toeplitz systems. They can be chosen as preconditioners themselves, or they can be used for the computation of...

In this paper we introduce the Cayley digraph structure. This can be considered as a generalization of Cayley digraph. We prove that all Cayley digraph structures are vertex transitive. Many graph theoretic properties are studied in terms of algebraic properties.

In a Cayley digraph on a group G, if a distinct colour is assigned to each arc-orbit under the left-regular action of G, it is not hard to show that the elements of the left-regular action of G are the only digraph automorphisms that preserve this colouring. In this paper, we show that the equivalent statement is not true in the most straightforward generalisation to G-vertex-transitive digraph...