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Papers by Abdul Jalil M. Khalaf
Advances in Mathematics
In this paper, we introduce and study some applications of a new class of univalent functions def... more In this paper, we introduce and study some applications of a new class of univalent functions defined by subordination property. Coefficient inequality, convex linear combinations, growth and distortion bounds, radii of starlikeness, convexity and close-to-convexity and Hadamard product (or convolution) are given.
This paper show that every wheel of even order n greater than or equal to 6 with three missing sp... more This paper show that every wheel of even order n greater than or equal to 6 with three missing spokes is chromatically unique.
In this paper, we introduce and study a new class of meromorphic Univalent functions defined by D... more In this paper, we introduce and study a new class of meromorphic Univalent functions defined by Dziok_Srivastava operator for this class. We obtain coefficient inequality, convex set, closure and Hadamard product (or convolution).Further we obtain a-neighborhood of the function , and the integral transform.
European Journal of Scientific Research
Let G be a simple graph andλ(G, λ) denotes the number of proper vertex colorings of with at most ... more Let G be a simple graph andλ(G, λ) denotes the number of proper vertex colorings of with at most λ colours, which is for a fixed graph G, a polynomial in λ, which is called the chromatic polynomial of G. By using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some biochemical structures.
The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative ... more The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x = 1 is equal to the Wiener index and second derivative at x =1 is equal to the hyperWiener index. In this paper we compute the Hosoya polynomial of some semiconducotors [Caesium Chloride, Perovskite structure, Zinc blende structure, Rock-salt(Nacl)structure, Wurtzite structure, Chalcopyrite structure], Wiener index and hyper-Wiener index for then. INTRODUCTION The graph polynomial which we study in this paper was invented in 1988 by Hosoya [6](and was originally named the Wiener polynomial). We nevertheless call it the Hosoya polynomial. It is defined as follows. Let G be a connected graph on n vertices. The vertex and edge sets of G are V(G) = {x 1 , x 2 , … , x n } and E(G) = {y 1 ; y 2 ,…, y m }, respectively. The length(= number of edges) of a shortest path between the vertices x i , x j ∈ V (G) is their distance and is denoted by d(x i , x j |G). The number of (unordered) pair...
Environmental Toxicology and Pharmacology, 2014
In the present study, we investigated the potential protective effects of royal jelly against aza... more In the present study, we investigated the potential protective effects of royal jelly against azathioprine-induced toxicity in rat. Intraperitoneal administration of azathioprine (50 mg/kgB.W.) induced a significant decrease in RBCs count, Hb concentration, PCV%, WBCs count, differential count and platelet count, hepatic antioxidant enzymes (reduced glutathione and glutathione s-transferase) and increase of serum transaminases (alanine aminotransferase and aspartate aminotransferase enzymes) activities, alkaline phosphatase and malondialdehyde formation. Azathioprine induced hepatotoxicity was reflected by marked pathological changes in the liver. Oral administration of royal jelly (200 mg/kgB.W.) was efficient in counteracting azathioprine toxicity whereas it altered the anemic condition, leucopenia and thrombocytopenia induced by azathioprine. Furthermore, royal jelly exerted significant protection against liver damage induced by azathioprine through reduction of the elevated activities of serum hepatic enzymes. Moreover, royal jelly blocked azathioprine-induced lipid peroxidation through decreasing the malondialdehyde formation. In conclusion, royal jelly possesses a capability to attenuate azathioprine-induced toxicity.
Let be a simple graph. set is a dominating set of , if every vertex in is adjacent to at least on... more Let be a simple graph. set is a dominating set of , if every vertex in is adjacent to at least one vertex in . Let be wheel with order n. Let be the family of dominating sets of a wheels with cardinality , and let . In this paper, we construct , and obtain a recursive formula for . Using this recursive formula, we consider the polynomial , which we call domination polynomial of wheels and obtain some properties of this polynomial.
In this paper, we introduce and study a new class of meromorphic multivalent functions defined by... more In this paper, we introduce and study a new class of meromorphic multivalent functions defined by integral operator for this class. We obtain coefficient inequality, like, linear combination, distortion Theorem and Hadamard product (or convolution). Further we obtain a ( , )-neighborhood of the function ∈ , and Radius of Starlikeness, Convexity and Close to Convexity.
Advances in Mathematics
In this paper, we introduce and study some applications of a new class of univalent functions def... more In this paper, we introduce and study some applications of a new class of univalent functions defined by subordination property. Coefficient inequality, convex linear combinations, growth and distortion bounds, radii of starlikeness, convexity and close-to-convexity and Hadamard product (or convolution) are given.
This paper show that every wheel of even order n greater than or equal to 6 with three missing sp... more This paper show that every wheel of even order n greater than or equal to 6 with three missing spokes is chromatically unique.
In this paper, we introduce and study a new class of meromorphic Univalent functions defined by D... more In this paper, we introduce and study a new class of meromorphic Univalent functions defined by Dziok_Srivastava operator for this class. We obtain coefficient inequality, convex set, closure and Hadamard product (or convolution).Further we obtain a-neighborhood of the function , and the integral transform.
European Journal of Scientific Research
Let G be a simple graph andλ(G, λ) denotes the number of proper vertex colorings of with at most ... more Let G be a simple graph andλ(G, λ) denotes the number of proper vertex colorings of with at most λ colours, which is for a fixed graph G, a polynomial in λ, which is called the chromatic polynomial of G. By using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some biochemical structures.
The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative ... more The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x = 1 is equal to the Wiener index and second derivative at x =1 is equal to the hyperWiener index. In this paper we compute the Hosoya polynomial of some semiconducotors [Caesium Chloride, Perovskite structure, Zinc blende structure, Rock-salt(Nacl)structure, Wurtzite structure, Chalcopyrite structure], Wiener index and hyper-Wiener index for then. INTRODUCTION The graph polynomial which we study in this paper was invented in 1988 by Hosoya [6](and was originally named the Wiener polynomial). We nevertheless call it the Hosoya polynomial. It is defined as follows. Let G be a connected graph on n vertices. The vertex and edge sets of G are V(G) = {x 1 , x 2 , … , x n } and E(G) = {y 1 ; y 2 ,…, y m }, respectively. The length(= number of edges) of a shortest path between the vertices x i , x j ∈ V (G) is their distance and is denoted by d(x i , x j |G). The number of (unordered) pair...
Environmental Toxicology and Pharmacology, 2014
In the present study, we investigated the potential protective effects of royal jelly against aza... more In the present study, we investigated the potential protective effects of royal jelly against azathioprine-induced toxicity in rat. Intraperitoneal administration of azathioprine (50 mg/kgB.W.) induced a significant decrease in RBCs count, Hb concentration, PCV%, WBCs count, differential count and platelet count, hepatic antioxidant enzymes (reduced glutathione and glutathione s-transferase) and increase of serum transaminases (alanine aminotransferase and aspartate aminotransferase enzymes) activities, alkaline phosphatase and malondialdehyde formation. Azathioprine induced hepatotoxicity was reflected by marked pathological changes in the liver. Oral administration of royal jelly (200 mg/kgB.W.) was efficient in counteracting azathioprine toxicity whereas it altered the anemic condition, leucopenia and thrombocytopenia induced by azathioprine. Furthermore, royal jelly exerted significant protection against liver damage induced by azathioprine through reduction of the elevated activities of serum hepatic enzymes. Moreover, royal jelly blocked azathioprine-induced lipid peroxidation through decreasing the malondialdehyde formation. In conclusion, royal jelly possesses a capability to attenuate azathioprine-induced toxicity.
Let be a simple graph. set is a dominating set of , if every vertex in is adjacent to at least on... more Let be a simple graph. set is a dominating set of , if every vertex in is adjacent to at least one vertex in . Let be wheel with order n. Let be the family of dominating sets of a wheels with cardinality , and let . In this paper, we construct , and obtain a recursive formula for . Using this recursive formula, we consider the polynomial , which we call domination polynomial of wheels and obtain some properties of this polynomial.
In this paper, we introduce and study a new class of meromorphic multivalent functions defined by... more In this paper, we introduce and study a new class of meromorphic multivalent functions defined by integral operator for this class. We obtain coefficient inequality, like, linear combination, distortion Theorem and Hadamard product (or convolution). Further we obtain a ( , )-neighborhood of the function ∈ , and Radius of Starlikeness, Convexity and Close to Convexity.