2016/11/23 by Xuanlong Ma, Min Feng, Ma, Xuanlong +3
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1611.07822
openalex publication_date 2016/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The \em power index Θ(Γ) of a graph Γ is the least order of a group G such that Γ can embed into the power graph of G. Furthermore, this group G is \em Γ-optimal if G has order Θ(Γ). We say that Γ is \em power-critical if its order equals to Θ(Γ). This paper focuses on the power indices of complete graphs, complete bipartite graphs and 1-factors. We classify all power-critical graphs Γ' in these three families, and give a necessary and sufficient condition for Γ'-optimal groups.