Topological Properties of Hexagonal Cage Networks (original) (raw)

Meshes and tori are widely used topologies for Network on chip (NoC). In this paper a new planar architecture called Hexagonal cage network HXCa(n) with two layers derived using two hexagonal meshes of same dimension. And a Hamiltonian cycle is shown in HXCa(4). In the last section a new operation called " Boundary vertex connection " (BVC) is introduced and conjectured that BVC of a 2-connected plane graph is Hamiltonian. For an ordered set M={m1,m2,m3,…,mp} of vertices in a connected graph G and a vertex u of G, the code of u with respect to M is the p-dimensional distance vector CM (u) = (d(v, m1), d(v, m2), d(v, m3),…,d(v, mp)). The set M is called the resolving set for G if d(x, m) ≠ d(y, m) for x, y in V \ M and m in M. A resolving set of minimum cardinality is called a minimum resolving set or a metric basis for G. The cardinality of the metric basis is called the metric dimension of G and is denoted by dim(G). In this paper the metric dimension problem is investigated for HXCa(n) Finding a metric basis and Hamiltonian cycle in a arbitrary graph is NP hard problem.