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Graphs from Subgraphs
Published in N. P. Shrimali, Nita H. Shah, Recent Advancements in Graph Theory, 2020
Joseph Varghese Kureethara, Johan Kok
If we remove some vertices from the existing graph, the resulting subgraph is known as an induced subgraph. If we randomly remove some edges, the resultant subgraph need not be an induced subgraph. Hence, a subgraph need not be an induced subgraph but all induced subgraphs are subgraphs. Induced subgraphs are studied extensively in the area of structural studies of graphs and networks. An excellent study on induced subgraphs is done with respect to the study of perfect graphs. A perfect graph is a graph such that for every induced subgraph of it, the clique number1 equals the chromatic number2 .
Graphene-based composites for biomedical applications
Published in Green Chemistry Letters and Reviews, 2022
Selsabil Rokia Laraba, Wei Luo, Amine Rezzoug, Qurat ul ain Zahra, Shihao Zhang, Bozhen Wu, Wen Chen, Lan Xiao, Yuhao Yang, Jie Wei, Yulin Li
Graphene is a carbon allotropic. It is described as one layer of carbon sheet with a hexagonal structural matrix with hybrid carbon atoms of the sp2 tightened up into a 2D wave grid-like structure, as shown in Figure 1, thereby offering a wide area on both sides of the linear axis. Graphene placed on the unmodified base band plane has free, hydrophobic electrons on the substrate. The hydrophobicity of the plot is, however, hugely reliant on the thickness, and single-layer graphene is much more hydrophilic than the thicker one (11). The perfect graph is a monolayer, covalent-bonded carbon atom. Graphene is the slimmest existing element that is capable of thermal conductivity at a high rate and has properties such as quantum hall effect, intrinsic strength, and high Young's modulus. A single graphene sheet without a gap possess properties of high electronic transportation, perfect optical transmission, barrier, and flame-retardant. It shows an ambitious electric field effect with gate voltage. A single sheet of graphene consumes 2.3% of radiation, and the material's shattering intensity is 42 N/m, according to a model of non-interrelating massless Dirac fermions. Other carbon allotropes have graphene as their base structure (12). TEM analysis of graphene nanoparticles revealed that Fe3O4 and Mn3O4 could be conveniently adjusted to change their particle diameter and coating densities by using different response times, as shown in Figure 2 (13).
Complexities in university students’ understanding of parametric equations and curves
Published in International Journal of Mathematical Education in Science and Technology, 2022
Vahid Borji, Hassan Alamolhodaei
Siavash constructed his schema at the trans stage. Excerpts of his answer to Task 1 are as follows. Siavash:Okay, I’ll determine the values ofandfor some values of the parameter, … [He correctly computesandfor the four values ofin a table], … I can sketch the parametric curve using these four points, … for sketching a perfect graph I also can find an equation between x and y by eliminating[He found the equation correctly], … Okay,is, … the graph is a parabola with the interval 0–3 on the x axis, … the direction of the curve is from, then,, and finally at, … like these arrows (Figure 6). Siavash used both the plotting method and eliminating method to sketch the parametric curve. It seems he has at least a Process conception of the concept. Siavash completely activated Pr0, Pr1, Pr2 and Pr3 during Task 1.