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The local minimum degree of a graph is the minimum degree reached by means of a series of local complementations. In this paper, we investigate on this quantity which plays an important role in quantum computation and quantum error correcting codes. First, we show that the local minimum degree of the Paley graph of order p is greater than √ p − 3 2 , which… (More)

A weak odd dominated (WOD) set in a graph is a subset B of vertices such that ∃D ⊆ V \B, ∀v ∈ B, |N (v)∩D| = 1 mod 2. We point out the connections of weak odd domination with odd domination, (σ, ρ)-domination, and perfect codes. We introduce bounds on κ(G), the maximum size of WOD sets of a graph G, and on κ ′ (G), the minimum size of non WOD sets of G.… (More)

A threshold ((k, n)) quantum secret sharing protocol [6, 2, 3] is a protocol by which a dealer distributes shares of a quantum secret to n players such that any subset of at least k players can access the secret, while any set of less than k players has no information about it. We investigate a particular family of quantum secret sharing protocols… (More)

An accessing set in a graph is a subset B of vertices such that ∃D ⊆ B, ∀v ∈ V \ B, |N (v) ∩ D| = 0 mod 2. In this paper, we introduce new bounds on the minimal size κ ′ (G) of an accessing set, and on the maximal size κ(G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly κ(G) and κ ′ (G) for several… (More)

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