A note on the Brush Number of Jaco Graphs, Jₙ(1), n ∈ N
Kok, Johan
Original · EN
The concept of the brush number bᵣ(G) was introduced for a simple connected undirected graph G. This note extends the concept to a special family of directed graphs and declares that the brush number bᵣ(Jₙ(1)) of a finite Jaco graph, Jₙ(1), n ∈ N with prime Jaconian vertex vᵢ is given by: bᵣ(Jₙ(1)) = ∑ⱼ₌₁ⁱ(d+(vⱼ) - d-(vⱼ)) + ∑ⱼ₌ᵢ₊₁ⁿmax{0, (n-j) - d-(vⱼ)}.
English translation
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