title: Variable neighborhood search for extremal graphs. 10. Comparison of irregularity indices for chemical trees.
abstract: 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 of Bell's 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 are characterized for the two last indices.
authors.affiliation: GERAD - Ecole des Hautes Etudes Commerciales, 3000, chemin de la Cote-Sainte-Catherine, Montréal, Quebec H3T 2A7, Canada.
authors.forename: Ivan
authors.initials: I
authors.lastname: Gutman
authors.forename: Pierre
authors.initials: P
authors.lastname: Hansen
authors.forename: Hadrien
authors.initials: H
authors.lastname: Mélot