The Fibonacci cube Γ n is the subgraph of the n-cube induced by the binary strings that
contain no two consecutive 1s. These graphs are applicable as interconnection networks …

The Fibonacci cube Γ n is the subgraph of hypercube Q n induced by the binary strings that
contain no two consecutive 1s, and the Lucas cube Λ n is obtained from Γ n by removing …

Abstract Let X⊆{0, 1} n. The daisy cube Q n (X) is introduced as the subgraph of Q n
induced by the union of the intervals I (x, 0 n) over all x∈ X. Daisy cubes are partial cubes …

In this paper, a new sub-family of Hypercubes called the Lucas-run graphs R nl are
introduced. The name of this new family of graphs is identified with the interesting fact that| V …

In this paper, we introduce the Pell graphs, a new family of graphs similar to the Fibonacci
cubes. They are defined on certain ternary strings (Pell strings) and turn out to be subgraphs …

The cube polynomial of a graph is the counting polynomial for the number of induced k-
dimensional hypercubes (k≥ 0). We determine the cube polynomial of Fibonacci cubes and …

We introduce alternate Lucas cubes, a new family of graphs designed as an alternative for
the well known Lucas cubes. These interconnection networks are subgraphs of Fibonacci …

We consider a q-analogue of the cube polynomial of Fibonacci cubes. These bivariate
polynomials satisfy a recurrence relation similar to the standard one. They refine the count of …

In this paper, generalized Pell graphs $\Pi _ {n, k} $, $ k\ge 2$, are introduced. The special
case of $ k= 2$ are the Pell graphs $\Pi _ {n} $ defined earlier by Munarini. Several metric …

Benzenoid systems or hexagonal systems are subgraphs of a hexagonal lattice. Open-
ended carbon nanotubes alias tubulenes can be seen as an embedding of a benzenoid …