We present embeddings of generalized ladders as subgraphs into the hypercube. By embedding caterpillars into ladders, we obtain embeddings of caterpillars into the hypercube. In this way we obtain almost all known results concerning the embeddings of caterpillars into the hypercube. In addition we construct embeddings for some new types of caterpillars.

The total embedding distributions of a graph is consisted of the orientable embeddings and nonorientable embeddings and have been know for few classes of graphs. The genus distribution of Ringel ladders is determined in [Discrete Mathematics 216 (2000) 235-252] by E.H. Tesar. In this paper, the explicit formula for non-orientable embeddings of Ringel ladders is obtained.

A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices with the same label contains a vertex with a larger label. The rank number of a graph is the fewest number of labels that can be used in a ranking. The rank number of a graph is known for many families, including the ladder graph P2 × Pn. We consider how ”bending” a ladder affects ...

The optical properties of Al nanostructures are investigated by means of time dependent density functional theory, considering chains of varying length and ladders/stripes of varying aspect ratio. The absorption spectra show redshifting for increasing length and aspect ratio. For the chains the absorption is dominated by HOMO → LUMO transitions, whereas ladders and stripes reveal more complex s...

A regular n-sided polygon can be split into n n-part spidrons. Alternate forms of linked triangular structures such as ladders and creepers can also be used to subdivide regular polygons. In the present paper new symmetric designs with inscribed regular polygons are constructed using n 6-part ladders. Also several new tiling patterns are created using these designs General Terms Tiling, Algorit...

Superconductivity has been recently observed in Sr 0.4 Ca 13.6 Cu 24 O 41.84 which contains quasi–one–dimensional Cu 2 O 3 2–leg ladders. If, as suggested by some theories, the superconductivity arises from these 2–leg ladders, it will be important to determine the structure of the superconducting gap. In particular, does the gap on a 2–leg ladder change sign when one goes from the bonding to a...

The title one-dimensional coordination network, {[Eu(2)(NO(3))(6)(C(10)H(8)N(2)O(2))(3)]·2CH(2)Cl(2)}(n), is isostructural with the previously reported Tb and Tl coordination networks and to its Gd analog. The Eu(III) cation is coordinated in a distorted tricapped trigonal-prismatic fashion by nine O atoms from three bridging 4,4'-bipyridine N,N'-dioxide ligands and three chelating nitrate anio...

Given to positive numbers a and b, we show how we easily can construct the power mean Pk(a, b) of order k for the cases k = −2, −1, −1/2, 0, 1/2, 1 and 2. This is done by observing that the power means correspond to certain distances in the crossed ladders problem. The so-called crossed ladders problem, of unknown origin, has been discussed in the literature at least since 1895 (see [3, p. 62-6...

Weak–coupling calculation of the gap structure of doped n–leg Hubbard ladders Abstract In weak coupling, the spin gap in doped, even, n–leg periodic Hubbard ladders reflects the energy to break a pair into separate quasiparticles. Here we investigate the structure of the gap within a spin–fluctuation exchange approximation. We also calculate the amplitude for removing a singlet pair from two la...