On the Lucas cubes. (English) Zbl 0987.05048
Some structural and enumerative properties of the Lucas cubes are determined in this paper. More precisely, these properties are the independence numbers of the edges and vertices, the radius, the center of the generating function of a sequence of numbers connected to the partite sets, the asymptotic behavior of the ratio of the numbers of edges and vertices. Some identities involving Fibonacci and Lucas numbers are obtained. The Lucas semilattices are introduced and their characteristic polynomials are found.
Reviewer: A.Rappoport (Landau)
Online Encyclopedia of Integer Sequences:
The edge independence number of the Lucas cube Lambda(n).Triangle read by rows: T(n,k) is the number of vertex pairs at distance k of the Lucas cube Lambda(n) (1<=k<=n).
The hyper-Wiener index of the Lucas cube Lambda(n) (n>=2).
Clique covering number, independence number, and Shannon capacity of the n-Lucas cube graph.