2012/10/19 by Pietro Codara, Codara, Pietro, Ottavio M. D’Antona +2
Computer Science · Engineering · Mathematics · #68R05 #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Interconnection Networks and Systems #cs.DM #graph theory and CDMA systems #math.CO #msc:68R05
paper · pdf · doi:10.48550/arxiv.1210.5561
9 pages, 4 figures
arxiv created 2012/10/19 · openalex publication_date 2012/10/19 · arxiv updated 2012/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the first part of this work we provide a formula for the number of edges of the Hasse diagram of the independent subsets of the h-th power of a path ordered by inclusion. For h=1 such a value is the number of edges of a Fibonacci cube. We show that, in general, the number of edges of the diagram is obtained by convolution of a Fibonacci-like sequence with itself. In the second part we consider the case of cycles. We evaluate the number of edges of the Hasse diagram of the independent subsets of the h-th power of a cycle ordered by inclusion. For h=1, and n>1, such a value is the number of edges of a Lucas cube.