Groupe d’études et de recherche en analyse des décisions


Variable Neighborhood Search for Extremal Graphs 10. Comparison of Irregularity Indices for Chemical Trees

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Chemical graphs, as other ones, are regular if all their vertices have the same degree. Otherwise, they are irregular and it is of interest to measure their irregularity both for descriptive purposes and for QSAR/QSPR studies. Three indices have been proposed in the literature for that purpose: those of Collatz-Sinogowitz, of Albertson and the variance of degrees. We study their properties for the case of chemical trees. Structural conjectures are generated with the system AutoGraphiX, and most of them proved later by mathematical means. Analytical expressions for extremal values are obtained and extremal graphs characterized for the two last indices.

, 25 pages

Ce cahier a été révisé en août 2004