TY  - JOUR
TI  - q-counting hypercubes in Lucas cubes
AB  - Lucas and Fibonacci cubes are special subgraphs of the binary hypercubes that have been proposed as modelsof interconnection networks. Since these families are closely related to hypercubes, it is natural to consider the nature ofthe hypercubes they contain. Here we study a generalization of the enumerator polynomial of the hypercubes in Lucascubes, whichq-counts them by their distance to the all 0 vertex. Thus, our bivariate polynomials re ne the count ofthe number of hypercubes of a given dimension in Lucas cubes and forq= 1 they specialize to the cube polynomials ofKlav zar and Mollard. We obtain many properties of these polynomials as well as theq-cube polynomials of Fibonaccicubes themselves. These new properties include divisibility, positivity, and functional identities for both families.
AU  - Egecioglu, Omer
AU  - Saygı, Elif
PY  - 2018
JO  - Turkish Journal of Mathematics
VL  - 42
IS  - 1
SN  - 1300-0098
SP  - 190
EP  - 203
DB  - TRDizin
UR  - http://search/yayin/detay/255904
ER  -