The degree sequence of Fibonacci and Lucas cubes
نویسندگان
چکیده
منابع مشابه
The degree sequence of Fibonacci and Lucas cubes
The Fibonacci cube Γn is the subgraph of the n-cube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained from Γn by removing vertices that start and end with 1. It is proved that the number of vertices of degree k in Γn and Λn is ∑k i=0 ( n−2i k−i )( i+1 n−k−i+1 ) and ∑k i=0 [ 2 ( i 2i+k−n )( n−2i−1 k−i ) + ( i−1 2i+k−n )( n−2i k−i )] , respectively. ...
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 کاملCube polynomial of Fibonacci and Lucas cubes
The cube polynomial of a graph is the counting polynomial for the number of induced k-dimensional hypercubes (k ≥ 0). We determine the cube polynomial of Fibonacci cubes and Lucas cubes, as well as the generating functions for the sequences of these cubes. Several explicit formulas for the coefficients of these polynomials are obtained, in particular they can be expressed with convolved Fibonac...
متن کاملAsymptotic properties of Fibonacci cubes and Lucas cubes
It is proved that the asymptotic average eccentricity and the asymptotic average degree of both Fibonacci cubes and Lucas cubes are (5 + √ 5)/10 and (5 − √ 5)/5, respectively. A new labeling of the leaves of Fibonacci trees is introduced and it is proved that the eccentricity of a vertex of a given Fibonacci cube is equal to the depth of the associated leaf in the corresponding Fibonacci tree. ...
متن کاملMaximal hypercubes in Fibonacci and Lucas cubes
The Fibonacci cube Γn is the subgraph of the hypercube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained 5 from Γn by removing vertices that start and end with 1. We characterize maximal induced hypercubes in Γn and Λn and deduce for any p ≤ n the number of maximal p-dimensional hypercubes in these graphs.
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: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.03.019