On the Szeged Index of Unbranched Catacondensed Benzenoid Molecules

The Szeged index (Sz) of unbranched catacondensed benzenoid (UBCB) hydrocarbons is examined. An efficient method for the calculations of their Sz is put forward. Among the UBCB molecules with a fixed number of hexagons, the linear polyacene has a rnaximal and the helicene a minimal Sz

Some results on the Wiener index related to the \v{S}olt\'{e}s problem of graphs

The Wiener index, $W(G)$, of a connected graph $G$ is the sum of distances between its vertices. In 2021, Akhmejanova et al. posed the problem of finding graphs $G$ with large $R_m(G)= |\{v\in V(G)\,|\,W(G)-W(G-v)=m \in \mathbb{Z} \}|/ |V(G)|$. It is shown that there is a graph $G$ with $R_m(G) > 1/2$ for any integer $m \ge 0$. In particular, there is a regular graph of even degree with this property for any odd $m \ge 1$. The proposed approach allows to construct new families of graphs $G$ with $R_0(G) \rightarrow 1/2$ when the order of $G$ increases.Comment: 9 pages, 3 tables, 7 figure

Explicit Relation between the Wiener Index and the Schultz Index of Catacondensed Benzenoid Graphs

The Wiener index (W) and the Schultz molecular topological index (MTI) are based on the distances between the vertices of chemical graphs. It is shown that MTI(G) = 5W(G) – (12h2 – 14h + 5) for an arbitrary catacondensed benzenoid graph G having h hexagons

Trees, Quadratic Line Graphs and the Wiener Index

The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a tree. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most (chemical trees). The line graph L(G) of a graph G has the vertex set V(L(G)) = E(G) and two distinct vertices of L(G) are adjacent if the corresponding edges of G have a common endvertex. It is known that the Wiener indices of a tree and of its line graph are always distinct. An infinite two-parameter family of growing chemical trees T with the property W(T) = W(L(L(T))) has been constructed

Some news about oblique graphs

A k-gon alpha of a polyhedral graph G(V,E,F) is of type if the vertices incident with alpha in cyclic order have degrees b1, b2,...,bk and $ is the lexicographic minimum of all such sequences available for alpha. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3

Analytical “Bake-Off” of Whole Genome Sequencing Quality for the Genome Russia Project Using a Small Cohort for Autoimmune Hepatitis

A comparative analysis of whole genome sequencing (WGS) and genotype calling was initiated for ten human genome samples sequenced by St. Petersburg State University Peterhof Sequencing Center and by three commercial sequencing centers outside of Russia. The sequence quality, efficiency of DNA variant and genotype calling were compared with each other and with DNA microarrays for each of ten study subjects. We assessed calling of SNPs, indels, copy number variation, and the speed of WGS throughput promised. Twenty separate QC analyses showed high similarities among the sequence quality and called genotypes. The ten genomes tested by the centers included eight American patients afflicted with autoimmune hepatitis (AIH), plus one case’s unaffected parents, in a prelude to discovering genetic influences in this rare disease of unknown etiology. The detailed internal replication and parallel analyses allowed the observation of two of eight AIH cases carrying a rare allele genotype for a previously described AIH-associated gene (FTCD), plus multiple occurrences of known HLA-DRB1 alleles associated with AIH (HLA-DRB1-03:01:01, 13:01:01 and 7:01:01). We also list putative SNVs in other genes as suggestive in AIH influence

Super-soft and super-elastic dry gels

Molecular combs and bottlebrushes are a new class of polymer architecture allowing for anomalously low density of entanglements in polymer melts. The conformations and rheological properties of melts of these branched macromolecule composed of a flexible backbone and side chains densely tethered to it are investigated theoretically, experimentally and by computer simulations.1,2 We develop the rule for dialing in the desired value of the melt plateau modulus of these molecules as low as 1000 times below the conventional values for linear polymer melts and experimentally verify the validity of our theory. The theory also predicts that elastomers made from these melts should be super-elastic and reversibly stretch up to ten times more than elastomers made from linear polymers. Hybrid networks with both permanent and reversible bonds made with this novel architecture are predicted to be super-tough and self-healing. References W.F.M. Daniel, J. Burdynska, M. Vatankhah-Varnoosfaderani, K. Matyjaszewski, J. Paturej, M. Rubinstein, A.V. Dobrynin and S.S. Sheiko, Nature Materials, 2016, 15, 183-190. L.H Cai, T.E. Kodger, R.E. Guerra, A.F. Pegoraro, M. Rubinstein, and D.A. Weitz, Advanced Materials 2015, 27, 5132–5140

Genome-wide sequence analyses of ethnic populations across Russia

The Russian Federation is the largest and one of the most ethnically diverse countries in the world, however no centralized reference database of genetic variation exists to date. Such data are crucial for medical genetics and essential for studying population history. The Genome Russia Project aims at filling this gap by performing whole genome sequencing and analysis of peoples of the Russian Federation. Here we report the characterization of genome-wide variation of 264 healthy adults, including 60 newly sequenced samples. People of Russia carry known and novel genetic variants of adaptive, clinical and functional consequence that in many cases show allele frequency divergence from neighboring populations. Population genetics analyses revealed six phylogeographic partitions among indigenous ethnicities corresponding to their geographic locales. This study presents a characterization of population-specific genomic variation in Russia with results important for medical genetics and for understanding the dynamic population history of the world's largest country

Chameleon-like elastomers with molecularly encoded strain-adaptive stiffening and coloration

Active camouflage is widely recognized as a soft-tissue feature, and yet the ability to integrate adaptive coloration and tissuelike mechanical properties into synthetic materials remains elusive. We provide a solution to this problem by uniting these functions in moldable elastomers through the self-assembly of linear-bottlebrush-linear triblock copolymers. Microphase separation of the architecturally distinct blocks results in physically cross-linked networks that display vibrant color, extreme softness, and intense strain stiffening on par with that of skin tissue. Each of these functional properties is regulated by the structure of one macromolecule, without the need for chemical cross-linking or additives. These materials remain stable under conditions characteristic of internal bodily environments and under ambient conditions, neither swelling in bodily fluids nor drying when exposed to air