Velocity and distance of neighbourhood sequences

Abstract

Das et al. [2] defined the notion of periodic neighbourhood sequences. They also introduced a natural ordering relation for such sequences. Fazekas et al. [4] generalized the concept of neighbourhood sequences, by dropping periodicity. They also extended the ordering to these generalized neighbourhood sequences. The relation has some unpleasant properties (e.g., it is not a complete ordering). In certain applications it can be useful to compare any two neighbourhood sequences. For this purpose, in the present paper we introduce a norm-like concept, called velocity, for neighbourhood sequences. This concept is in very close connection with the natural ordering relation. We also define a metric for neighbourhood sequences, and investigate its properties.