Abstract:
In this paper we consider some problems in combinatorial analysis related to placements without neighbours on graphs, namely, we find numbers and probabilities of such placements for simplest graphs (segment, two segments, cycle), and also (which is more difficult) we solve the same problems for a cycle up to rotations.
Keywords:recurrence relations, Fibonacci numbers, Fibonacci polynomials, Lucas numbers, Lucas polynomials.
Fulltext:
PDF file (147 kB)