Gaussian networks are degree four symmetric networks and these are designed based on the concept of Gaussian integers. The Gaussian network can be described in terms of a generator α = α + bi, where a and bare integers and i = √-1 . When gcd(a,b) = 1, how to find edge disjoint Hamiltonian cycles has been shown before. In this paper for any generator α = α + bi, even when gcd(a,b) = d > 1, how to obtain two edge disjoint Hamiltonian cycles in these networks is described.

In this paper, we show that the hexagonal mesh networks developed in the early 1990s are a special case of the EJ networks that have been considered more recently. Using a node addressing scheme based on the EJ number system, we give a shortest path routing algorithm for hexagonal mesh networks. We also extend the known efficient one-to-all broadcasting algorithm on hexagonal mesh networks to algorithms for one-to-one personalized broadcasting, all-to-all broadcasting, and all-to-all personalized broadcasting algorithms. Their time complexity and optimality are analyzed.