2025/11/26 by Fei Ma, Ma, Fei
Computer Science · Mathematics · #05C09 #05C76 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2511.21426
openalex publication_date 2025/11/26 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28
Graph is considered neutral if its assortativity coefficient r is equal to zero. In this paper, we address an outstanding conjecture, i.e., whether is there a neutral graph on n vertices? First, we show that for n≥7, there is at least one neutral tree, which suggests that we find a representative of any order neutral graph. Additionally, we obtain that given n≥13, there exists at least one neutral non-tree graph.