65 research outputs found
Further study on forbidden subgraphs of power graph
The undirected power graph (or simply power graph) of a group , denoted by
, is a graph whose vertices are the elements of the group , in which
two vertices and are adjacent if and only if either or
for some positive integers , . Forbidden subgraph has a significant role
in graph theory. In our previous work \cite{cmm}, we consider five important
classes of forbidden subgraphs of power graph which include perfect graphs,
cographs, chordal graphs, split graphs and threshold graphs. In this
communication, we go even further in that way. This study, inspired by the
articles \cite{celmmp,dong,ck}, examines additional significant forbidden
classes, including chain graphs, diamond-free graphs, -free graphs and -free graph. The finite groups whose power graphs are chain graphs,
diamond-free graphs, and -free
graphs have been successfully identified in this work. In case of -free graphs, we completely determine all the nilpotent
groups, direct product of two groups, finite simple groups whose power graph is
-free.Comment: 20 page
Intersection subgroup graph with forbidden subgraphs
Let be a group. The intersection subgroup graph of (introduced by
Anderson et al. \cite{anderson}) is the simple graph whose
vertices are those non-trivial subgroups say of with
for some non-trivial subgroup of ; two distinct vertices and are
adjacent if and only if , where is the identity element of
. In this communication, we explore the groups whose intersection subgroup
graph belongs to several significant graph classes including cluster graphs,
perfect graphs, cographs, chordal graphs, bipartite graphs, triangle-free and
claw-fee graphs. We categorize each nilpotent group so that
belongs to the above classes. We entirely classify the simple group of Lie type
whose intersection subgroup graph is a cograph. Moreover, we deduce that
is neither a cograph nor a chordal graph if is a
torsion-free nilpotent group
Co-maximal subgroup graph characterized by forbidden subgraphs
In this communication, the co-maximal subgroup graph of a finite
group is examined when is a finite nilpotent group, finite abelian
group, dihedral group , dicyclic group , and -group. We derive
the necessary and sufficient conditions for to be a cluster graph,
triangle-free graph, claw-free graph, cograph, chordal graph, threshold graph
and split graph. For the case of finite nilpotent group, we are able to
classify it entirely. Moreover, we derive the complete structure of finite
abelian group such that is a split graph. We leave the readers
with a few unsolved questions
Optical and electrical properties of undoped and doped Ge nanocrystals
Size-dependent photoluminescence characteristics from Ge nanocrystals embedded in different oxide matrices have been studied to demonstrate the light emission in the visible wavelength from quantum-confined charge carriers. On the other hand, the energy transfer mechanism between Er ions and Ge nanocrystals has been exploited to exhibit the emission in the optical fiber communication wavelength range. A broad visible electroluminescence, attributed to electron hole recombination of injected carriers in Ge nanocrystals, has been achieved. Nonvolatile flash-memory devices using Ge nanocrystal floating gates with different tunneling oxides including SiO2, Al2O3, HfO2, and variable oxide thickness [VARIOT] tunnel barrier have been fabricated. An improved charge storage characteristic with enhanced retention time has been achieved for the devices using VARIOT oxide floating gate
Improved infrared photoluminescence characteristics from circularly ordered self-assembled Ge islands
The formation of circularly ordered Ge-islands on Si(001) has been achieved because of nonuniform strain field around the periphery of the holes patterned by focused ion beam in combination with a self-assembled growth using molecular beam epitaxy. The photoluminescence (PL) spectra obtained from patterned areas (i.e., ordered islands) show a significant signal enhancement, which sustained till 200 K, without any vertical stacking of islands. The origin of two activation energies in temperature-dependent PL spectra of the ordered islands has been explained in detail
A source of entangled photons based on a cavity-enhanced and strain-tuned GaAs quantum dot
A quantum-light source that delivers photons with a high brightness and a
high degree of entanglement is fundamental for the development of efficient
entanglement-based quantum-key distribution systems. Among all possible
candidates, epitaxial quantum dots are currently emerging as one of the
brightest sources of highly entangled photons. However, the optimization of
both brightness and entanglement currently requires different technologies that
are difficult to combine in a scalable manner. In this work, we overcome this
challenge by developing a novel device consisting of a quantum dot embedded in
a circular Bragg resonator, in turn, integrated onto a micromachined
piezoelectric actuator. The resonator engineers the light-matter interaction to
empower extraction efficiencies up to 0.69(4). Simultaneously, the actuator
manipulates strain fields that tune the quantum dot for the generation of
entangled photons with fidelities up to 0.96(1). This hybrid technology has the
potential to overcome the limitations of the key rates that plague current
approaches to entanglement-based quantum key distribution and
entanglement-based quantum networks. Introductio
Structural and optical properties of germanium nanostructures on Si(100) and embedded in high-k oxides
International Conference on Mathematical Modelling and Scientific Computing
This book contains original research papers presented at the International Conference on Mathematical Modelling and Scientific Computing, held at the Indian Institute of Technology Indore, India, on 19–21 July 2018. Organized into 30 chapters, the book presents the recent progress and the most advanced innovations, trends, and real-world challenges encountered and solutions embraced in the applications of mathematics and scientific computing. The book will be of interests to a wide variety of researchers, students and the practicing engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics, vibration problem, computer science, and numerical optimization to physics, chemistry, biology, electrical, civil, mechanical, chemical, seismology, aerospace, and medical sciences. The aim of the conference is to bring together leading academicians, scientists, researchers, engineers, and industry partners from all over the globe to exchange and share their experiences and research results on various aspects of applied mathematics and scientific computation, like, differential equation, modeling, simulation, dynamical systems, numerical analysis, matrix theory, inverse problems, and solid and fluid mechanics, computational engineering
Catalytic Asymmetric Direct Vinylogous Michael Addition of Deconjugated Butenolides to Maleimides for the Construction of Quaternary Stereogenic Centers
Competition under control: A practical and efficient direct asymmetric vinylogous Michael reaction of deconjugated butenolides has been developed (see scheme). The products of this reaction, highly functionalized chiral succinimides, are obtained in excellent yield with high diastereoselectivity (up to d.r.=18:1) and outstanding enantioselectivity (up to e.r.=99.5:0.5)
Remarkable influence of secondary catalyst site on enantioselective desymmetrization of cyclopentenedione
An efficient, robust and highly enantioselective catalytic desymmetrization of 2,2-disubstituted cyclopentene-1,3-diones is developed via direct vinylogous nucleophilic addition of deconjugated butenolides. A remarkable influence of the secondary catalyst site on the enantioselectivity points towards an intriguing mechanistic scenario, possibly by triggering a change in catalyst conformation
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