Generalized Lucas cubes
نویسندگان
چکیده
منابع مشابه
Generalized Lucas cubes
Let f be a binary string and d C 1. Then the generalized Lucas cube Qd(JÐf ) is introduced as the graph obtained from the d-cube Qd by removing all vertices that have a circulation containing f as a substring. The question for which f and d, the generalized Lucas cube Qd(JÐf ) is an isometric subgraph of the d-cube Qd is solved for all binary strings of length at most five. Several isometricall...
متن کاملConnectivity of Fibonacci cubes, Lucas cubes, and generalized cubes
If f is a binary word and d a positive integer, then the generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all the vertices that contain f as a factor, while the generalized Lucas cube Qd( ↽Ð f ) is the graph obtained from Qd by removing all the vertices that have a circulation containing f as a factor. The Fibonacci cube Γd and the Lucas cube Λd are the grap...
متن کاملOn the Lucas Cubes
A Lucas cube 3^ can be defined as the graph whose vertices are the binary strings of length n without either two consecutive l's or a 1 in the first and in the last position, and in which the vertices are adjacent when their Hamming distance is exactly 1. A Lucas cube 5E„ is very similar to the Fibonacci cube Tn which is the graph defined as 2J, except for the fact that the vertices are binary ...
متن کاملOn the Wiener index of generalized Fibonacci cubes and Lucas cubes
The generalized Fibonacci cube Qd(f) is the graph obtained from the d-cube Qd by removing all vertices that contain a given binary word f as a factor; the generalized Lucas cube Qd( ↽Ð f ) is obtained from Qd by removing all the vertices that have a circulation containing f as a factor. In this paper the Wiener index of Qd(1) and the Wiener index of Qd( ↽Ð 1) are expressed as functions of the o...
متن کاملThe (non-)existence of perfect codes in Lucas cubes
A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring. Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$. For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applicable Analysis and Discrete Mathematics
سال: 2012
ISSN: 1452-8630,2406-100X
DOI: 10.2298/aadm120108002i