Calculating the permanent of a (0, 1) matrix is a #P -complete problem but there are some classes of structuredmatrices for which the permanent is calculable in polynomial time. The most well-known example is the fixedjump (0, 1) circulant matrix which, using algebraic techniques, was shown by Minc to satisfy a constant-coefficient fixed-order recurrence relation. In this note we show how, by i...

A connected ρ-regular graph G has largest eigenvalue ρ in modulus. G is called Ramanujan if it has at least 3 vertices and the second largest modulus of its eigenvalues is at most 2 √ ρ− 1. In 2010 Droll classified all Ramanujan unitary Cayley graphs. These graphs of type ICG(n, {1}) form a subset of the class of integral circulant graphs ICG(n,D), which can be characterised by their order n an...

With the objective of employing graphs toward a more generalized theory of signal processing, we present a novel sampling framework for (wavelet-)sparse signals defined on circulant graphs which extends basic properties of Finite Rate of Innovation (FRI) theory to the graph domain, and can be applied to arbitrary graphs via suitable approximation schemes. At its core, the introduced Graph-FRI-f...

We show in this paper that the circulant graph G( 2”‘, 4) is Hamiltonian decomposable, and propose a recursive construction method. This is a partial answer to a problem posed by B. Alspach. @ 1997 Published by Elsevier Science B.V.

Graph embedding problems have gained importance in the field of interconnection networks for parallel computer architectures. In this paper, we determine the exact wirelength and dilation of embedding circulant networks into k-rooted sibling trees. AMS Subject Classification: 05C78, 05C85

We give an efficient construction of a reasonably small dominating set in a circulant graph on n notes and k distinct chord lengths. This result is based on bounds on some double exponential sums.

Recent developments in commutative algebra, linear and graph theory allow us to approach various issues several fields. Circulant graphs now have a wider range of practical uses, including as the foundation for optical networks, discrete cellular neural small-world models chemical reactions, supercomputing multiprocessor systems. Herein, we are concerned with decompositions bipartite circulant ...

In this paper, we study the existence of cycles of all lengths in the recursive circulant graphs, and we show a necessary and sufficient condition for the graph being pancyclic and bipancyclic.  2002 Elsevier Science B.V. All rights reserved.