2015/01/15 by Johan Kok, Kok, Johan, C Susanth +4
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #math.CO
paper · pdf · doi:10.48550/arxiv.1501.03623
5 pages. arXiv admin note: substantial text overlap with arXiv:1501.01381
arxiv created 2015/01/15 · openalex publication_date 2015/01/15 · arxiv updated 2015/01/16 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
The concept of the brush number br(G) was introduced for a simple connected undirected graph G. The concept will be applied to the Mycielskian graph μ(G) of a simple connected graph G to find br(μ(G)) in terms of an optimal orientation of G. We prove a surprisingly simple general result for simple connected graphs on n ≥ 2 vertices namely: br(μ(G))= br(μ→(G)) = 2∑i=1nd+_G→br(G)(vi).