A note on the Brush Number of Jaco Graphs, J_n(1), n ∈ \Bbb N

2014/12/18 by Johan Kok, Kok, Johan
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1412.5733

7 pages

arxiv created 2014/12/18 · arxiv updated 2014/12/19

Abstract

The concept of the brush number b_r(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 b_r(J_n(1)) of a finite Jaco graph, J_n(1), n ∈ \Bbb N with prime Jaconian vertex v_i is given by: b_r(J_n(1)) = ∑_j=1^I(d⁺(v_j) - d^-(v_j)) + ∑_j=I+1ⁿmax\0, (n-j) - d^-(v_j)\.

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