Fibonacci polynomials and parity domination in grid graphs
Analogously to the sequence of Fibonacci numbers also the sequence of Fibonacci polynomials is defined. They are polynomials of one variable \(x\) over the field of real numbers or over some Galois field. In any case the sequence of Fibonacci polynomials \(f_0,f_1,f_2,\dots\) is defined recurrently so that \(f_0= 0\), \(f_1=1\), \(f_i= f_{i-1}+ xf_{i-2}\) for \(i\geq 2\). In the paper Fibonacci polynomials over the Galois field \(\text{GF}(2)\) are used to investigate even domination in grid graphs. An even dominating set in a graph \(G\) is a set \(S\) with the property that each vertex of \(G\) is adjacent to an even number of vertices of \(S\) (coinciding vertices are also considered as adjacent).
scientific article; zbMATH DE number 1773378