  Spanning trees are widely used in networks for broadcasting, fault-tolerance,
and securely delivering messages. Hexagonal interconnection networks have a
number of real life applications. Examples are cellular networks, computer
graphics, and image processing. Eisenstein-Jacobi (EJ) networks are a
generalization of hexagonal mesh topology. They have a wide range of potential
applications, and thus they have received researchers' attention in different
areas among which interconnection networks and coding theory. In this paper, we
present two spanning trees' constructions for Eisenstein-Jacobi (EJ). The first
constructs three edge-disjoint node-independent spanning trees, while the
second constructs six node-independent spanning trees but not edge disjoint.
Based on the constructed trees, we develop routing algorithms that can securely
deliver a message and tolerate a number of faults in point-to-point or in
broadcast communications. The proposed work is also applied on higher
dimensional EJ networks.
