The notion of the circular coloring signed graphs is a recent one that simultaneously extends both notions and $0$-free graphs. A $r$-coloring graph $(G, \sigma)$ to assign points circle circumference $r$, $r\geq 2$, vertices $G$ such connected by positive edge are at distance least $1$ negative most $\frac{r}{2}-1$. infimum all $r$ for which admits said be chromatic number denoted $\chi_c(G, \...

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...

The girth of a finitely generated group G is defined to be the supremum of the girth of its Cayley graphs. Let G be a finitely generated subgroup of the mapping class group ModΣ, where Σ is an orientable closed surface with a finite number of punctures and with a finite number of components. We show that G is either a non-cyclic group with infinite girth or a virtually free-abelian group; these...