Walking backward: walk counts of negative order.
A closed formula is derived for walk counts of negative order k in a graph or molecule, as defined recently by Lukovits and Trinajstić. Some unexpected observations made by these authors easily follow from this formula. Gratifyingly, the formula is very similar to the one obtained earlier for usual walk counts. Moreover, while for walk counts of k --> + infinity the numerically largest eigenvalue of the adjacency matrix plays an important part, for walk counts of k --> - infinity the numerically smallest eigenvalue plays a corresponding part.
Rücker
Gerta
G
Department of Rehabilitative and Preventative Sports Medicine, Universität Freiburg, Hugstetter Strasse 55, D-79106 Freiburg, Germany. ruecker@msm1.ukl.uni-freiburg.de
Rücker
Christoph
C