Small vertex-transitive graphs of given degree and girth

We investigate the basic interplay between the small k-valent vertex-transitive graphs of girth g and the (k, g)-cages, the smallest k-valent graphs of girth g. We prove the existence of k-valent Cayley graphs of girth g for every pairof parameters k ≥ 2 and g ≥ 3, improve the lower bounds on the order of the smallest (k, g) vertex-transitive graphs forcertain families with prime power girth, and generalize the construction of Bray, Parker and Rowley that has yielded several of the smallest known (k, g)-graphs

Behavior of Petrie Lines in Certain Edge-Transitive Graphs

We survey the construction and classification of one-, two- and infinitely-ended members of a class of highly symmetric, highly connected infinite graphs. In addition, we pose a conjecture concerning the relationship between the Petrie lines and ends of some infinitely-ended members of this class

A Themed Issue Dedicated to Professor John B. Goodenough on the Occasion of His 100th Birthday Anniversary

This book of Molecules is dedicated to Professor John B. Goodenough (born July 25, 1922, Jena, Germany), an American physicist, who won the 2019 Nobel Prize for Chemistry for his work on developing lithium-ion batteries

INSERTION (CO)POLYMERIZATION OF OLEFINS CATALYZED BY FIRST ROW TRANSITION METAL COMPLEXES

Since polyolefins are an integral part of everyday life and given the ever-growing global demand for these polymers, the insertion polymerization of olefins is one of the most industrially relevant synthetic reaction, widely investigated also in academia. It is in this context that this PhD project is located. The developed research activity was aimed at synthesizing new catalytic systems capable of stereochemically drive the polymerization of various (di)olefins, in particular cyclic olefins such as norbornene and its derivatives. The investigated catalysts are made up of two components: the organometallic complex (pre-catalyst) and an aluminum alkyl compound (co-catalyst or activator). Among the series of the organometallic complexes, during my PhD, complexes of the first row transition metals, i.e., titanium, vanadium, and chromium, bearing nitrogen and phosphorous based ligands were investigated. They were later applied as catalysts for the homopolymerization of ethylene, cyclic olefins (norbornene, dicyclopentadiene and norbornene derivatives) and 1,3-butadiene, and the copolymerization of ethylene with various cyclic olefins. Depending on the employed catalyst and the polymerization conditions, we obtained oligomers or high-polymers. All the products were carefully characterized with different techniques, in order to get more information on the properties of the obtained (co)polymers as well as on the polymerization mechanism. Norbornene and dicyclopentadiene oligomers were mainly obtained from titanium and chromium catalysts, activated by Et2AlCl and methylalumoxane (MAO), respectively, while cyclic olefin copolymers were obtained from the copolymerization of ethylene with cyclic olefins promoted by vanadium based catalysts. In addition, we demonstrated that some vanadium and chromium complexes, in combination with MAO, were active in the polymerization of 1,3-butadiene, affording poly(1,3-butadiene) with different microstructure (cis-1,4, trans-1,4 or 1,2) and stereospecificity (i.e., iso- or syndiotactic polymers), depending on the type of ligand. This study allowed to understand the correlations between the catalyst\u2019s features and the polymerization outcome in terms of activity, regio- and stereoselectivity. Moreover, particular emphasis has been devoted to the study of the catalyst stability over the polymerization time and temperature. At the same time, particular interest has been developed toward the post\uf02dpolymerization functionalization, as a strategy to modify some polymer properties (e.g., solubility and processability) and thus to obtain polymers hardly obtainable by direct (co)polymerization with polar (co)monomers. This PhD dissertation reports the results achieved during the three-year research activity, together with the main difficulties encountered and the actions put in place trying to overcome them

IN SILICO METHODS FOR DRUG DESIGN AND DISCOVERY

Computer-aided drug design (CADD) methodologies are playing an ever-increasing role in drug discovery that are critical in the cost-effective identification of promising drug candidates. These computational methods are relevant in limiting the use of animal models in pharmacological research, for aiding the rational design of novel and safe drug candidates, and for repositioning marketed drugs, supporting medicinal chemists and pharmacologists during the drug discovery trajectory.Within this field of research, we launched a Research Topic in Frontiers in Chemistry in March 2019 entitled “In silico Methods for Drug Design and Discovery,” which involved two sections of the journal: Medicinal and Pharmaceutical Chemistry and Theoretical and Computational Chemistry. For the reasons mentioned, this Research Topic attracted the attention of scientists and received a large number of submitted manuscripts. Among them 27 Original Research articles, five Review articles, and two Perspective articles have been published within the Research Topic. The Original Research articles cover most of the topics in CADD, reporting advanced in silico methods in drug discovery, while the Review articles offer a point of view of some computer-driven techniques applied to drug research. Finally, the Perspective articles provide a vision of specific computational approaches with an outlook in the modern era of CADD