The Total Number of Maximal \(k\)-Independent Sets in the Generalized Lexicographical Product of Graphs

Abstract

In this paper, we determine the number of all maximal \(k\)-independent sets in the generalized lexicographical product of graphs. We construct a polynomial that calculates this number using the concept of Fibonacci polynomials and generalized Fibonacci polynomials. Also, for special graphs, we give the recurrence formula.