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 ≤ ⌊log
₂
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 ≤ ⌊log
₂
n⌋. We show that 2 ⌊ 1/2 ⌈ n-2/2
_Δ
- 2 ⌉⌋ + 1 ≤ b(W
_{δ, n}
) ≤ ⌈ n-2/2
_Δ
- 2⌉ + Δ-1.