Sufficient conditions for fractional [a,b]-deleted graphs

Let $a$ and $b$ be two positive integers with $a\leq b$, and let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$. Let $h:E(G)\rightarrow[0,1]$ be a function. If $a\leq\sum\limits_{e\in E_G(v)}{h(e)}\leq b$ holds for every $v\in V(G)$, then the subgraph of $G$ with vertex set $V(G)$ and edge set $F_h$, denoted by $G[F_h]$, is called a fractional $[a,b]$-factor of $G$ with indicator function $h$, where $E_G(v)$ denotes the set of edges incident with $v$ in $G$ and $F_h=\{e\in E(G):h(e)>0\}$. A graph $G$ is defined as a fractional $[a,b]$-deleted graph if for any $e\in E(G)$, $G-e$ contains a fractional $[a,b]$-factor. The size, spectral radius and signless Laplacian spectral radius of $G$ are denoted by $e(G)$, $\rho(G)$ and $q(G)$, respectively. In this paper, we establish a lower bound on the size, spectral radius and signless Laplacian spectral radius of a graph $G$ to guarantee that $G$ is a fractional $[a,b]$-deleted graph.Comment: 1

Signless Laplacian spectral radius for a k-extendable graph

Let $k$ and $n$ be two nonnegative integers with $n\equiv0$ (mod 2), and let $G$ be a graph of order $n$ with a 1-factor. Then $G$ is said to be $k$-extendable for $0\leq k\leq\frac{n-2}{2}$ if every matching in $G$ of size $k$ can be extended to a 1-factor. In this paper, we first establish a lower bound on the signless Laplacian spectral radius of $G$ to ensure that $G$ is $k$-extendable. Then we create some extremal graphs to claim that all the bounds derived in this article are sharp.Comment: 11 page

Spectral radius and k-factor-critical graphs

For a nonnegative integer $k$, a graph $G$ is said to be $k$-factor-critical if $G-Q$ admits a perfect matching for any $Q\subseteq V(G)$ with $|Q|=k$. In this article, we prove spectral radius conditions for the existence of $k$-factor-critical graphs. Our result generalises one previous result on perfect matchings of graphs. Furthermore, we claim that the bounds on spectral radius in Theorem 3.1 are sharp.Comment: 12 page

Molecular cloning and expression analysis of a zebrafish novel zinc finger protein gene rnf141

ZNF230 is a novel zinc finger gene cloned by our laboratory. In order to understand the potential functions of this gene in vertebrate development, we cloned the zebrafish orthologue of human ZNF230, named rnf141. The cDNA fragment of rnf141 was obtained by rapid amplification of cDNA ends (RACE). The open reading frame (ORF) encodes a polypeptide of 222 amino acids which shares 75.65% identity with the human ZNF230. RT-PCR analysis in zebrafish embryo and adult tissues revealed that rnf141 transcripts are maternally derived and that rnf141 mRNA has a broad distribution. Zygotic rnf141 message is strongly localized in the central nervous system, as shown by whole-mount in situ hybridization. Knockdown and over expression of rnf141 can induce abnormal phenotypes, including abnormal development of brain, as well as yolk sac and axis extendsion. Marker gene analysis showed that rnf141 may play a role in normal dorsoventral patterning of zebrafish embryos, suggesting that rnf141 may have a broad function during early development of vertebrates

Identification of novel mutations in Chinese Hans with autosomal dominant polycystic kidney disease

<p>Abstract</p> <p>Background</p> <p>Autosomal dominant polycystic kidney disease (ADPKD) is the most common inherited renal disease with an incidence of 1 in 400 to 1000. The disease is genetically heterogeneous, with two genes identified: <it>PKD1 </it>(16p13.3) and <it>PKD2 </it>(4q21). Molecular diagnosis of the disease in at-risk individuals is complicated due to the structural complexity of <it>PKD1 </it>gene and the high diversity of the mutations. This study is the first systematic ADPKD mutation analysis of both <it>PKD1 </it>and <it>PKD2 </it>genes in Chinese patients using denaturing high-performance liquid chromatography (DHPLC).</p> <p>Methods</p> <p>Both <it>PKD1 </it>and <it>PKD2 </it>genes were mutation screened in each proband from 65 families using DHPLC followed by DNA sequencing. Novel variations found in the probands were checked in their family members available and 100 unrelated normal controls. Then the pathogenic potential of the variations of unknown significance was examined by evolutionary comparison, effects of amino acid substitutions on protein structure, and effects of splice site alterations using online mutation prediction resources.</p> <p>Results</p> <p>A total of 92 variations were identified, including 27 reported previously. Definitely pathogenic mutations (ten frameshift, ten nonsense, two splicing defects and one duplication) were identified in 28 families, and probably pathogenic mutations were found in an additional six families, giving a total detection level of 52.3% (34/65). About 69% (20/29) of the mutations are first reported with a recurrent mutation rate of 31%.</p> <p>Conclusions</p> <p>Mutation study of <it>PKD1 </it>and <it>PKD2 </it>genes in Chinese Hans with ADPKD may contribute to a better understanding of the genetic diversity between different ethnic groups and enrich the mutation database. Besides, evaluating the pathogenic potential of novel variations should also facilitate the clinical diagnosis and genetic counseling of the disease.</p

Sufficient conditions for graphs to have strong parity factors

A graph G has a strong parity factor F if for every subset X ⊆ V (G) with |X| even, G contains a spanning subgraph F such that δ(F) ≥ 1, dF(u) ≡ 1 (mod 2) for any u ∈ X, and dF(v) ≡ 0 (mod 2) for any v ∈ V (G)\X. In this article, we first provide a size condition for a graph having a strong parity factor. Then we put forward a toughness condition to guarantee that a graph has a strong parity factor