Alexandru T. Balaban | Searcharxiv

arXiv2019

Two new topological indices based on graph adjacency matrix eigenvalues and eigenvectors

The Estrada topological index EE, based on the eigenvalues of the adjacency matrix, is degenerate for cospectral graphs. By additionally considering the eigenvectors, two new topological indices are devised (RV_a and RV_b), which have reduced degeneracy for alkanes or cyclic graphs. Index RV_a shows similarity to EE in ordering of alkanes with 8 to 10 carbon atoms, whereas index RV_b is more similar to the average distance-based connectivity (Balaban index J). Inter-correlations between these four topological indices are discussed, indicating which factors have predominant influence.

math.SP↗

arXiv2015

Energies for cyclic and acyclic aggregations of adamantane and diamantane units sharing vertices, edges, or six-membered rings

Diamondoids are hydrocarbons having a carbon scaffold comprised from polymer-like composites of adamantane cages. The present paper describes computed total energies and "SWB-tension" energies (often referred to as "strain" energies) for species having $n$ adamantane or diamantane units sharing pairwise: one carbon atom (spiro-[n]adamantane or spiro-[$n$]diamantane); one C-C bond (one-bond-sharing-[$n$]adamantane or one-bond-sharing-[$n$]diamantane); or one chair-shaped hexagon of carbon atoms (1234-helical-cata-[$n$]diamantanes). Each of the five investigated polymer-like types is considered either as an acyclic or a cyclic chain of adamantane- or diamantane-unit cages. With increasing $n$ values, SWB-tension energies for acyclic aggregates are found to increase linearly, while the net SWB-tension energies of cyclic aggregates often go thru a minimum at a suitable value of $n$. In all five cases, a limiting common energy per unit ($E/n$ ) is found to be approached by both cyclic and acyclic chains as $n\to \infty $, as revealed from plots of $E/n$ versus $1/n$ for acyclic chains and of $E/n$ versus $1/n^2$ for cyclic chains.

physics.chem-ph↗