Let T be an n-vertex tree and e its edge. By n1(e|T) and n2(e|T) are denoted the number of vertices of T lying on the two sides of e; n1(e|T) + n2(e|T) = n. Conventionally, n1(e|T) ≤ n2(e|T). If T′ and T′′ are two trees with the same number n of vertices, and if their edges e1′,e2′,l,en-1′ and e1′′,e2′′,l,en-1′′ can be labelled so that n1(ei′|T′) = n1(ei′′|T′′) holds for all i=1,2,l,n–1, then T′ and T′′ are said to be equiseparable. Several previously studied molecular–graph–based structure–descriptors have equal values for equiseparable trees, which is a disadvantageous property of these descriptors. In earlier works large families of equiseparable trees have been found. We now show that equiseparability is ubiquitous, and that almost all trees have an equiseparable mate. The same is true for chemical trees.

In this work, we suggested a new approach for the basic configuration of a mobile robot capable of being a building block of an intelligent agent. This configuration includes obstacle avoidance (OA), goal tracking (DTG) and communication implemented as competence layers. Moreover, a geometry based behavior arbitration layer is proposed for fusing those behaviors. Proposed control is tested on simulations where different scenarios are studied. Results have confirmed the high performance of the method.