TY - JOUR
JF - scj
JO - SCJ
VL - 5
IS - 1
PY - 2017
Y1 - 2017/3/01
TI - Metric and Combinatorial Properties of Fibonacci and Lucas cubes
N2 - An n-dimensional hypercube, Q_n, is a graph in which vertices are binary strings of length n where two vertices are adjacent if they differ in exactly one coordinate. Hypercubes and their subgraphs have a lot of applications in different fields of science, specially in computer science. This is the reason why they have been investigated by many authors during the years. Some of their subgraphs named Fibonacci cubes and Lucas cubes are very important and are useful in interconnection networks. In this paper, after introducing these cubes, we report their metric and combinatorial properties done by different authors. Then, we present some open problems that we have been encountered during our research regarding these cubes. Finally, we briefly introduce the software named Sage which is very applicable in the calculations for theses cubes in high dimensions.
SP - 78
EP - 100
AU - Fathalikhani, Khadijeh
AU - Ashrafi, Ali Reza
AD - University of Kashan
KW Hypercube
KW Fibonacci cube
KW Lucas cube.
UR - http://scj.kashanu.ac.ir/article-1-295-en.html
ER -