Fibonacci cubes are defined as subgraphs of hypercubes, where the vertices are those without two consecutive 1's in their binary string representation. $k$-Fibonacci cubes are in turn special subgraphs of Fibonacci cubes obtained by eliminating certain edges. This elimination is carried out at the step analogous to where the fundamental recursion is used to construct Fibonacci cubes themselves from the two previous cubes by link edges. In this work, we calculate the vertex chromatic polynomial of $k$-Fibonacci cubes for $k=1,2$. We also determine the domination number and the total domination number of $k$-Fibonacci cubes for $n,k \leq 12$ by using an integer programming formulation.
Hypercube, Fibonacci cube, Fibonacci number, $k$-Fibonacci cube, vertex coloring, domination
EĞECİOĞLU, ÖMER; SAYGI, ELİF; and SAYGI, ZÜLFÜKAR
"On the chromatic polynomial and the domination number of $k$-Fibonacci cubes,"
Turkish Journal of Mathematics: Vol. 44:
5, Article 23.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/23