Assessment of Oxidative Stress in Peste Des Petits Ruminants (Ovine Rinderpest) Affected Goats

The aim of the present investigation was to evaluate oxidative stress in goats affected with peste des petits ruminants (PPR). The experiment was designed to collect blood samples from PPR affected as well as healthy goats during a series of PPR outbreaks which occurred during February to April 2012 in different districts of Rajasthan state (India). Out of total 202 goats of various age groups and of both the sexes, 155 goats were PPR affected and 47 were healthy. Oxidative stress was evaluated by determining various serum biomarkers viz. vitamin A, vitamin C, vitamin E, glutathione, catalase, superoxide dismutase, glutathione reductase and xanthine oxidase, the mean values of which were 1.71±0.09 µmol L-1, 13.02±0.14 µmol L-1, 2.22±0.09 µmol L-1, 3.03±0.07 µmol L-1, 135.12±8.10 kU L-1, 289.13±8.00 kU L-1, 6.11± 0.06 kU L-1 and 98.12±3.12 mU L-1, respectively. Each parameter analysis of variance showed highly significant effect (P=0.0001) of health status and age category. Further interaction between health status and age category was also highly significant (P=0.0001) for each parameter studied. The results indicated that vitamins A, C, E and glutathione levels depressed by 18.95%, 38.67%, 47.64%, and 47.39%, respectively and the serum catalase, superoxide dismutase, glutathione reductase and xanthine oxidase activities increased by 90.79%, 75.11%, 90.34%, and 44.06%, respectively in affected animals as compared to that in healthy ones. On the basis of the altered levels of serum biomarkers of oxidative stress it was concluded that the animals affected with PPR developed oxidative stress

A Characterisation of Weak Integer Additive Set-Indexers of Graphs

An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. An integer additive set-indexer is said to be $k$-uniform if $|g_f(e)| = k$ for all $e\in E(G)$. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ for all $u,v\in V(G)$. In this paper, we study the characteristics of certain graphs and graph classes which admit weak integer additive set-indexers.Comment: 12pages, 4 figures, arXiv admin note: text overlap with arXiv:1311.085

A Study on Topological Integer Additive Set-Labeling of Graphs

A set-labeling of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(X)$, where $X$ is a finite set and a set-indexer of $G$ is a set-labeling such that the induced function $f^{\oplus}:E(G)\to \mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\oplus}(uv) = f(u){\oplus}f(v)$ for every $uv{\in} E(G)$ is also injective. Let $G$ be a graph and let $X$ be a non-empty set. A set-indexer $f:V(G)\to \mathcal{P}(X)$ is called a topological set-labeling of $G$ if $f(V(G))$ is a topology of $X$. An integer additive set-labeling is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$, whose associated function $f^+:E(G)\to \mathcal{P}(\mathbb{N}_0)$ is defined by $f(uv)=f(u)+f(v), uv\in E(G)$, where $\mathbb{N}_0$ is the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ is its power set. An integer additive set-indexer is an integer additive set-labeling such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. In this paper, we extend the concepts of topological set-labeling of graphs to topological integer additive set-labeling of graphs.Comment: 16 pages, 7 figures, Accepted for publication. arXiv admin note: text overlap with arXiv:1403.398

Weak Integer Additive Set-Indexers of Certain Graph Products

An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. If $g_f(uv)=k \forall uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexers. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|g_f(uv)|=max(|f(u)|,|f(v)|) \forall uv\in E(G)$. We have some characteristics of the graphs which admit weak integer additive set-indexers. We already have some results on the admissibility of weak integer additive set-indexer by certain graphs and finite graph operations. In this paper, we study further characteristics of certain graph products like cartesian product and corona of two weak IASI graphs and their admissibility of weak integer additive set-indexers and provide some useful results on these types of set-indexers.Comment: 7 pages, arXiv admin note: text overlap with arXiv:1310.6091, arXiv:1311.0345, submitte

A Study on Integer Additive Set-Graceful Graphs

A set-labeling of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(X)$, where $X$ is a finite set and a set-indexer of $G$ is a set-labeling such that the induced function $f^{\oplus}:E(G)\rightarrow \mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\oplus}(uv) = f(u){\oplus}f(v)$ for every $uv{\in} E(G)$ is also injective. An integer additive set-labeling is an injective function $f:V(G)\rightarrow \mathcal{P}(\mathbb{N}_0)$, $\mathbb{N}_0$ is the set of all non-negative integers and an integer additive set-indexer is an integer additive set-labeling such that the induced function $f^+:E(G) \rightarrow \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective. In this paper, we extend the concepts of set-graceful labeling to integer additive set-labelings of graphs and provide some results on them.Comment: 11 pages, submitted to JARP

Further Studies on the Sparing Number of Graphs

Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. If $f^+(uv)=k~\forall~uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=\max(|f(u)|,|f(v)|)~\forall ~ uv\in E(G)$. In this paper, we study the admissibility of weak integer additive set-indexer by certain graphs and graph operations.Comment: 10 Pages, Submitted. arXiv admin note: substantial text overlap with arXiv:1310.609

On Integer Additive Set-Indexers of Graphs

A set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \rightarrow2^{X}$ such that the function $f^{\oplus}:E(G)\rightarrow2^{X}-\{\emptyset\}$ defined by $f^{\oplus}(uv) = f(u){\oplus} f(v)$ for every $uv{\in} E(G)$ is also injective, where $2^{X}$ is the set of all subsets of $X$ and $\oplus$ is the symmetric difference of sets. An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective. A graph $G$ which admits an IASI is called an IASI graph. An IASI $f$ is said to be a {\em weak IASI} if $|g_f(uv)|=max(|f(u)|,|f(v)|)$ and an IASI $f$ is said to be a {\em strong IASI} if $|g_f(uv)|=|f(u)| |f(v)|$ for all $u,v\in V(G)$. In this paper, we study about certain characteristics of inter additive set-indexers.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1312.7674 To Appear in Int. J. Math. Sci.& Engg. Appl. in March 201