Domination Number of the Non-commuting Graph of Finite Groups

Let G be a non-abelian group. The non-commuting graph of group G, shown by ΓG, is a graph with the vertex set G \ Z(G), where Z(G) is the center of group G. Also two distinct vertices of a and b are adjacent whenever ab ≠ ba. A set S ⊆ V(Γ) of vertices in a graph Γ is a dominating set if every vertex v ∈ V(Γ) is an element of S or adjacent to an element of S. The domination number of a graph Γ denoted by γ(Γ), is the minimum size of a dominating set of Γ. </p><p>Here, we study some properties of the non-commuting graph of some finite groups. In this paper, we show that \gamma(\Gamma_G)<\frac{|G|-|Z(G)|}{2}. Also we charactrize all of groups G of order n with t = ∣Z(G)∣, in which $\gamma(\Gamma_{G})+\gamma(\overline{\Gamma}_{G})\in \{n-t+1,n-t,n-t-1,n-t-2\}.

Biochemical Investigation of Different Extracts and Larvicidal Activity of Tagetes minuta L. on Anopheles stephensi Larvae: Larvicidal activity of extracts of Tagetes minuta

Tagetes minuta L. is considered as an annual plant growing in the temperate zones of South America. It has been used as carminative, anti-inflammatory, anti-abortion, vermifuge, bronchodilator and hypotensive. In the current study the locally cultured plant of Tagetes minuta L. was studied for phytochemical and larvicidal properties. The phytochemical analysis of aerial parts of the plant exhibited the presence of saponins, terpenoids, tannins, alkaloids and flavonoids. The efficacy of methanolic extract of the plant was tested against malaria vector, Anopheles stephensi. The probit analysis from the concentration and mortality exhibited the LC50 and LC90 values of 2.5 mg/l and 11.0 mg/l, respectively. Also the efficacies of the ethyl acetate, chloroform, methanolic and aqueous extracts of the plant were tested on Anopheles stephensi with the LC50 concentration of the methanolic extract. The results showed that the chloroform extract had the highest efficacy

Chemical Composition and Repellent Activity of Achillea vermiculata and Satureja hortensis against Anopheles stephensi

Background: One of the best ways to control the malaria disease and to be protected human against Anopheles mos­quito biting is the use of repellents. Throughout repellents, herbal ones may be an appropriate and safe source for protection. Methods: Chemical constituents of Achillea vermiculata and Satoreja hortensis were determined by using gas chromatography-mass spectrometry. Efficacy and the protection time of these plants were assessed on Anopheles stephensi under the laboratory condition. Results: The mean assessed protection time and efficacy for A. vermiculata was 2.16 and 3.16 hours respectively and the obtained ED50 and ED90 for this plant was 5.67 and 63 µl/cm2 respectively. The figured for S. hortensis was 4.16 and 5 hours respectively.  ED50 and ED90 for this plant were 5.63 and 45.75µl/cm2 respectively. Conclusion: Results of investigation showed that S. hortensis plant has an acceptable protection time, therefore, this plant could be considered as a good herbal repellent against anopheles mosquitoes