  A Fibonacci string is a length n binary string containing no two consecutive
1s. Fibonacci cubes (FC), Extended Fibonacci cubes (ELC) and Lucas cubes (LC)
are subgraphs of hypercube defined in terms of Fibonacci strings. All these
cubes were introduced in the last ten years as models for interconnection
networks and shown that their network topology posseses many interesting
properties that are important in parallel processor network design and parallel
applications. In this paper, we propose a new family of Fibonacci-like cube,
namely Extended Lucas Cube (ELC). We address the following network simulation
problem : Given a linear array, a ring or a two-dimensional mesh; how can its
nodes be assigned to ELC nodes so as to keep their adjacent nodes near each
other in ELC ?. We first show a simple fact that there is a Hamiltonian path
and cycle in any ELC. We prove that any linear array and ring network can be
embedded into its corresponding optimum ELC (the smallest ELC with at least the
number of nodes in the ring) with dilation 1, which is optimum for most cases.
Then, we describe dilation 1 embeddings of a class of meshes into their
corresponding optimum ELC.
