In this note we present House of Graphs (http://hog.grinvin.org) which is a new database of graphs. The key principle is to have a searchable database and offer -next to complete lists of some graph classes -also a list of special graphs that already turned out to be interesting and relevant in the study of graph theoretic problems or as counterexamples to conjectures. This list can be extended by users of the database.

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.

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