Nov 14, 2017: Fengwei Li: Graph parameters and chemistry: the augmented Zagreb index

November 14, 2017Graph parameters and chemistry: the augmented Zagreb index
Room: Hal B 2AFengwei Li

In theoretical chemistry and biology, molecular descriptors are used for modeling structural information of molecules, with the purpose of capturing interesting physical and chemical properties of these molecules in single numerical values. These molecular descriptors are also referred to as topological indices. Over the years, many topological indices have been introduced.  In this presentation, we introduce and study the augmented Zagreb index (AZI index for short), which has been proven to be a valuable predictive index in the study of the heat of formation in octanes and heptanes. We give an expression for the AZI index of f-benzenoid systems in terms of their inlet features, and deduce the minimal and maximal value of the AZI index over the set of cata-catacondensed f-benzenoid systems. We also discuss the minimal values of the AZI indices of f-benzenoid systems with a given number of hexagons.  Finally, we present several sharp upper bounds on the AZI index of graphs with fixed parameters such as the independence number, the edge-connectivity and the chromatic number respectively, and characterize the corresponding extremal graphs.