Broadcasting in the Kno¨del graph

The broadcast time of a graph G, denoted 6(G), is the minimum time necessary to complete the broadcasting in G, i.e. from one of vertices send a message to all other vertices. The Knödel graph W_{Δ, n} is a regular graph of an even order n and degree Δ where 2 ≤ Δ ≤ ⌊log₂ n⌋. The broadcast time of the Knödel graph is known only for W _δ,2Δ and for W _{Δ-1, 2Δ-1}. In this paper we present a tight upper and lower bounds on the broadcast time of the Knödel graph for all even n and 2 ≤ Δ ≤ ⌊log₂ n⌋. We show that 2 ⌊ 1/2 ⌈ n-2/2_Δ - 2 ⌉⌋ + 1 ≤ b(W_{δ, n}) ≤ ⌈ n-2/2_Δ - 2⌉ + Δ-1.