Effects on fractional domination in graphs

 A graph G is an undirected finite connected graph. A function f : V (G) → [0, 1] is called a fractional dominating function if, ∑ u∈N[v] f (u) ≥1, for all v ∈ V, where N [v] is the closed neighborhood of v. The weight of a fractional dominating function is w (f) = ∑ v∈V(G) f (v). The fractional domination number γ f  (G) has the least weight of all the fractional dominating functions of G. In this paper, we analyze the effects on γ f  (G) of deleting a vertex from G. Additionally, some bounds on γ f  (G) are discussed, and provide the exactness of some bounds. If we remove any leaves from any tree T, then the resulting graphs are , where |l| is the number of leaves. Some of the results are proved by the eccentricity value of a vertex e (v).

VGGNet-Cnn based classification of white blood cell leukemia with efficient salp swarm optimization algorithm

White blood cell (WBC) leukemia is caused by an excess of leukocytes in the bone marrow, and image-based identification of malignant WBCs is important for its detection. This research describes a new hybrid technique for accurate classification of WBC leukemia. To increase the image quality, the preprocessing is done using Contrast Limited Adaptive Histogram Equalization (CLAHE). The images are then segmented using Hidden Markov Random Fields (HMRF). To extract features from WBC images, Visual Geometry Group Network (VGGNet), a powerful Convolutional Neural Network (CNN) architecture, is used After that, an Efficient Salp Swarm Algorithm (ESSA) is used to optimize the extracted features. The proposed method is tested on two Acute Lymphoblastic Leukemia Image Databases, yielding good accuracy of 98.1% for dataset 1 and 98.8% for dataset 2. While enhancing accuracy, the ESSA optimization picked just 1K out of 25K features retrieved with VGGNet. The combination of CNN feature extraction with ESSA feature optimization could be effective for a variety of additional image classification tasks.

Solutions of Detour Distance Graph Equations

Graph theory is a useful mathematical structure used to model pairwise relations between sensor nodes in wireless sensor networks. Graph equations are nothing but equations in which the unknown factors are graphs. Many problems and results in graph theory can be formulated in terms of graph equations. In this paper, we solved some graph equations of detour two-distance graphs, detour three-distance graphs, detour antipodal graphs involving with the line graphs.

Germination induced changes in bioactive compounds and nutritional components of millets

The present study was conducted to compare the nutritional quality and the concentration of bioactive compounds in the flours from dehusked and germinated foxtail, barnyard, and little millets. Germinated millet flours showed significantly higher protein content (11.79-33.49%), total free amino acid content (66-334.87%) and protein solubility (13.83-34%), compared to the dehusked millet flours. The total phenols and flavonoids in the flours from the three germinated millets were significantly higher by about 142.36 and 437.20%, respectively, compared to the flours from the dehusked millets. Mineral content was also found to be higher in the flours from germinated millets in comparison to the flours from dehusked millets. The results of this study showed that the flours from the germinated millets have the potential for their application in development of novel products,because of their enhanced nutritional value. The extracts from the germinated millets have the potential for use as functional ingredients in the development of novel processed fruit beverages.

The connected monophonic eccentric domination number of a graph

A set S ⊆ V in a graph G is a MED-set if every vertex in V - S has a monophonic eccentric vertex in S. The MED-number γ me  (G) is the cardinality of a minimum MED-set of G. A set S ⊆ V in a graph G is a CMED-set if S is a MED-set and the induced subgraph is connected. The CMED-number γ cme  (G) is the cardinality of a minimum CMED-set of G. We investigate some properties of the CMED-sets. Also, we determine the bounds of the CMED-number and find the same for some standard graphs. The CMED-number has applications in security based communication networks in real life situations. This motivated us to introduce and investigate CMED-set in a graph.

Ultrasonic treatment stimulates multiple shoot regeneration and explant enlargement in recalcitrant squash cotyledon explants in vitro

Ultrasonic treatment (0.5-2 min) stimulated multiple shoot regeneration to high levels in vitro from recalcitrant cotyledon explants of commercial squash (Cucurbita pepo L.) cultivars Ma'yan and Bareqet, on Murashige and Skoog [Physiol Plant 15:473-497, 1962] (regeneration) medium augmented with 4.4 microM benzyladenine. At this stage, unsonicated control explants regenerated only a few very small shoots or bud-like structures. Ultrasound also stimulated massive explant growth. Ultrasound treatment resulted in further multiple shoot production (five times greater than control) after explant transfer to elongation medium (Murashige and Skoog [Physiol Plant 15:473-497, 1962] medium with 0.44 microM benzyladenine and 2.9 microM gibberellic acid). Longer ultrasonic treatments (5 or 10 min) promoted multiple shoot regeneration and explant growth accompanied by hyperhydration. Scanning electron microscope observations showed that 2 min ultrasound changed the joint area between epidermal cells and removed some of the surface from the cotyledon epidermal cells, without gross surface injury to the explants. Longer periods of ultrasound (5-10 min) caused further surface erosion. Rubbing the explant contact surface with chloroform or sandpaper emulated the effect of sonication on shoot regeneration and explant growth, demonstrating that ultrasound exerts its morphogenic influence by surface removal. Sonication of explants from other batches of squash seeds (of cultivars Ma'yan and True French), that regenerated without such treatment, reduced regeneration and caused hyperhydration. This is the first report of stimulation of in vitro regeneration by ultrasound treatment.

Transgenic Acacia sinuata from Agrobacterium tumefaciens-mediated transformation of hypocotyls

Transgenic herbicide tolerant Acacia sinuata plants were produced by transformation with the bar gene conferring phosphinothricin resistance. Precultured hypocotyl explants were infected with Agrobacterium tumefaciens strain EHA105 in the presence of 100 microM acetosyringone and shoots regenerated on MS (Murashige and Skoog, 1962, Physiol Plant 15:473-497) medium with 13.3 microM benzylaminopurine, 2.6 microM indole-3-acetic acid, 1 g l(-1) activated charcoal, 1.5 mg l(-1) phosphinothricin, and 300 mg l(-1) cefotaxime. Phosphinothricin at 1.5 mg l(-1) was used for the selection. Shoots surviving selection on medium with phosphinothricin expressed GUS. Following Southern hybridization, eight independent shoots regenerated of 500 cocultivated explants were demonstrated to be transgenic, which represented transformation frequency of 1.6%. The transgenics carried one to four copies of the transgene. Transgenic shoots were propagated as microcuttings in MS medium with 6.6 microM 6-benzylaminopurine and 1.5 mg l(-1) phosphinothricin. Shoots elongated and rooted in MS medium with gibberellic acid and indole-3-butyric acid, respectively both supplemented with 1.5 mg l(-1) phosphinothricin. Micropropagation of transgenic plants by microcuttings proved to be a simple means to bulk up the material. Several transgenic plants were found to be resistant to leaf painting with the herbicide Basta.