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Article Dans Une Revue European Journal of Combinatorics Année : 2019

Daisy cubes and distance cube polynomial

Résumé

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.
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Dates et versions

hal-01526465 , version 1 (23-05-2017)

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Sandi Klavžar, Michel Mollard. Daisy cubes and distance cube polynomial: Dedicated to the memory of our friend Michel Deza. European Journal of Combinatorics, 2019, 80, pp.214-223. ⟨10.1016/j.ejc.2018.02.019⟩. ⟨hal-01526465⟩
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