TY - JOUR
T1 - Metric and Combinatorial Properties of Fibonacci and Lucas cubes
JF - scj
JO - scj
VL - 5
IS - 1
UR - http://scj.kashanu.ac.ir/article-1-295-en.html
Y1 - 2017
SP - 78
EP - 100
KW Hypercube
KW Fibonacci cube
KW Lucas cube.
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.
M3
ER -