2024/08/27 by Takayuki Hibi, Sara Saeedi Madani, Hibi, Takayuki +1
Computer Science · Mathematics · #05C12 #05C40 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2408.15141
openalex publication_date 2024/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite simple non-complete connected graph on [n] = \1, …, n\ and κ(G) ≥ 1 its vertex connectivity. Let f(G) denote the number of free vertices of G and diam(G) the diameter of G. The final goal of this paper is to determine all sequences of integers (n,f,d,k) with n≥ 8, f≥ 0, d≥ 2 and k≥ 1 for which there exists a finite simple non-complete connected graph on [n] with f=f(G), d=diam(G) and k=κ(G).