2017/05/24 by Sandi Klavžar, Klavžar, Sandi, Michel Mollard +1 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1705.08674
openalex publication_date 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X ⊆ 0, 1 n. Then the daisy cube Q n (X) is introduced as the sub-graph of Q n induced by the intersection of the intervals I(x, 0 n) over all x ∈ X. Daisy cubes are partial cubes that include Fibonacci cubes, Lucas cubes, and bipartite wheels. If u is a vertex of a graph G, then the distance cube polynomial D G,u (x, y) is introduced as the bivariate polynomial that counts the number of induced subgraphs isomorphic to Q k at a given distance from the vertex u. It is proved that if G is a daisy cube, then D G,0 n (x, y) = C G (x + y -- 1), where C G (x) is the previously investigated cube polynomial of G. It is also proved that if G is a daisy cube, then D G,u (x, --x) = 1 holds for every vertex u in G.