Eccentric connectivity index

The eccentric connectivity index $\xi^c$ is a novel distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as $\xi^c (G) = \sum_{v \in V (G)} deg (v) \cdot \epsilon (v)$\,, where $deg (v)$ and $\epsilon (v)$ denote the vertex degree and eccentricity of $v$\,, respectively. We survey some mathematical properties of this index and furthermore support the use of eccentric connectivity index as topological structure descriptor. We present the extremal trees and unicyclic graphs with maximum and minimum eccentric connectivity index subject to the certain graph constraints. Sharp lower and asymptotic upper bound for all graphs are given and various connections with other important graph invariants are established. In addition, we present explicit formulae for the values of eccentric connectivity index for several families of composite graphs and designed a linear algorithm for calculating the eccentric connectivity index of trees. Some open problems and related indices for further study are also listed.Comment: 25 pages, 5 figure

Molecular description for magnesium iodide

Graph theory, which has become a powerful area of mathematics, owns much advancement in the field of mathematical chemistry. Recently, chemical graph theory has turned into a very popular area among researchers because of its wide-ranging applications in the field of mathematical chemistry. The manipulation and inspection of chemical structural information is made feasible using molecular descriptors. The molecular topological descriptors are the numerical invariants of a molecular graph and are valuable for predicting their bioactivity. An abundant variety of such indices are taken into consideration and used in pharmaceutical researchers, in theoretical chemistry, in drugs and in several other fields. A topological index actually relates a chemical structure by means of a numeric number. In this recent research work, we have considered the chemical graph of magnesium iodide. We computed degree based topological indices. Mainly, we addressed atom-bond connectivity index (ABC), geometric arithmetic index (GA), fourth atom-bond connectivity index (ABC4), The fifth geometric-arithmetic index (GA5), general Randic' index Ra(G) and First Zagreb index M1(G), Second Zagreb index M2(G) for magnesium iodide, MgI2. Furthermore, the results are analysed and we have provided general formulas for all these above mentioned families of graphs that are in fact very helpful in studying the underlying topologies

Degree-Based Topological Indices

The degree of a vertex of a molecular graph is the number of first neighbors of this vertex. A large number of molecular-graph-based structure descriptors (topological indices) have been conceived, depending on vertex degrees. We summarize their main properties, and provide a critical comparative study thereof. (doi: 10.5562/cca2294

Floristic composition as an indicator of destabilisation of lowland forest ecosystems in Posavina

Background and Purpose: The succession of forests in the Posavina region follows a pattern from forests of black alder and ash through stands of pedunculate oak to pedunculate oak-hornbeam forests. In the past hundred years, this lowland area has been affected by a number of factors, among which anthropogenic influences hold a primary position. This has resulted in a considerable deviation from normal, natural succession. The purpose of this paper is to analyse the present condition, the degree of destabilisation and the future developmental trends of pedunculate oak stands by drawing on previous pedological, hydrological and vegetational research. One of the best indicators of the above is the ecoindicator values of the floristic composition. Materials and Methods: Phytocoenological relevés were taken in 25 localities of both stable and destabilised forest ecosystems of pedunculate oak in Žutica Forest. The principles of the Zurich-Montpellier School were applied for this process. The numerical analysis was carried out by means of SYN-TAX 2000 software. JUICE 6.3 and CANOCO 4.5 were also used to process the relevés, construct the phytocoenological tables and correlate species compositions and vegetation typeswith ecological factors. The obtained results were compared with the results of earlier ecological research. Results: Phytocoenological research revealed significant changes in the floristic composition. Ecoindicator values of plant species indicate a substantial change in ecological parameters and increased destabilisation, which leads to larger quantities of light, thermophilicity and humidity in sites. In addition, the sites are richer in nitrogen and the soil reaction becomes more basophilic, while central European species replace intermediary ones. Conclusions: The investigated plots show a regression process contrary to the normal direction of vegetation development in lowland areas. A return has been observed from the final community to transitional communities, and in some localities even to initial and pioneer communities

Survey on topological indices and graphs associated with a commutative ring

The researches on topological indices are initially related to graphs obtained from biological activities or chemical structures and reactivity. Recently, the research on this topic has evolved on graphs in general and even on graphs obtained from algebraic structures, such as groups, rings or modules. This paper will present various topological index concepts, various graph concepts obtained from a commutative ring and some previous studies that are relevant to those two concepts. Based on the various concepts presented, research topics related to topological indices of a graph associated with a commutative ring can be found and carried out

Structuprint: a scalable and extensible tool for two-dimensional representation of protein surfaces

© 2016 Kontopoulos et al.Background: The term molecular cartography encompasses a family of computational methods for two-dimensional transformation of protein structures and analysis of their physicochemical properties. The underlying algorithms comprise multiple manual steps, whereas the few existing implementations typically restrict the user to a very limited set of molecular descriptors. Results: We present Structuprint, a free standalone software that fully automates the rendering of protein surface maps, given - at the very least - a directory with a PDB file and an amino acid property. The tool comes with a default database of 328 descriptors, which can be extended or substituted by user-provided ones. The core algorithm comprises the generation of a mould of the protein surface, which is subsequently converted to a sphere and mapped to two dimensions, using the Miller cylindrical projection. Structuprint is partly optimized for multicore computers, making the rendering of animations of entire molecular dynamics simulations feasible. Conclusions: Structuprint is an efficient application, implementing a molecular cartography algorithm for protein surfaces. According to the results of a benchmark, its memory requirements and execution time are reasonable, allowing it to run even on low-end personal computers. We believe that it will be of use - primarily but not exclusively - to structural biologists and computational biochemists