We describe two new algorithms for the generation of all non-isomorphic cubic graphs with girth at least k ≥ 5 which are very efficient for 5 ≤ k ≤ 7 and show how these algorithms can be efficiently restricted to generate snarks with girth at least k. Our implementation of these algorithms is more than 30, respectively 40 times faster than the previously fastest generator for cubic graphs with ...

Mangroves are important in protecting and stabilizing coastal zones. Pneumatophores of the mangrove species Avicennia marina can form a large aboveground complex aerial roots, which supporting growth low-oxygen environments. We examined relationship between tree height, girth, sediment mud content, oxygen levels with pneumatophore abundance. As sediments higher content have more anaerobic condi...

We consider superfluous elements in a bounded lattice with 0 and 1, introduce various types of graphs associated these elements. The notions such as element graph (S(L)), join intersection (JI(L)) lattice, distributive (SI(L)) are defined. Dual atoms play an important role to find connections between the lattice-theoretic properties those corresponding graph-theoretic properties. Consequently, ...

AIM The aim was to study the polymorphism of exon 2 and exon 3 of growth hormone (GH) gene, to test the polymorphic variants for Hardy-Weinberg equilibrium and to investigate association of these polymorphisms with chest girth and paunch girth in Sirohi and Barbari breeds of goat. MATERIALS AND METHODS A total of 80 kids involving forty each of Sirohi and Barbari breeds of goat were included ...

The aim of this study is to estimate body weight from withers height, body length, and chest girth measurements by using Regression Tree (RT) Method. For this purpose, data were collected from 239 male sheep at yearling age (11-13 months) of five indigenous sheep breeds (Mengali (48), Balochi (48), Harnai (48), Beverigh (47) and Rakhshani (48)) reared in Balochistan, Pakistan. Bivariate relatio...

W. He et al. showed that a planar graph of girth 11 can be decomposed into a forest and a matching. D. Kleitman et al. proved the same statement for planar graphs of girth 10. We further improve the bound on girth to 9. c © 2007 Elsevier Ltd. All rights reserved.

This paper describes the calculation of the optimal partition parameters such that the girth maximum (m, r) Balanced Tanner Unit lies in family of BTUs specified by them using a series of proved results and thus creates a framework for specifying a search problem for finding the girth maximum (m, r) BTU. Several open questions for girth maximum (m, r) BTU have been raised.

Recently, we [1] proposed a simple-to-implement heuristic, namely, BIT-FILLING, for constructing high rate and high girth LDPC codes. In the present work, we extend BIT-FILLING, and demonstrate that the extended algorithm produces better codes, that is, codes with higher rate/girth and good bit error rate performance. We demonstrate the positive effect of girth on bit error rate performance.

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...