2017/09/06 by Yujia Jin, Huan Li, Zhongzhi Zhang · 17 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Computer science #Discrete mathematics #Dominating set #Domination analysis #Gene Regulatory Network Analysis #Graph #Graph theory and applications #Matching (statistics) #Mathematics #Tower #Vertex (graph theory) #cs.DM #math.CO
paper · pdf · doi:10.1016/j.tcs.2017.08.024
published in Theoretical Computer Science 703, 37-54 (Elsevier BV)
openalex publication_date 2017/09/06 · arxiv created 2017/09/13 · arxiv updated 2017/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Apollonian networks display the remarkable power-law and small-world properties as observed in most realistic networked systems. Their dual graphs are extended Tower of Hanoi graphs, which are obtained from the Tower of Hanoi graphs by adding a special vertex linked to all its three extreme vertices. In this paper, we study analytically maximum matchings and minimum dominating sets in Apollonian networks and their dual graph- s, both of which have found vast applications in various fields, e.g. structural controllability of complex networks. For both networks, we determine their matching number, domination number, the number of maximum matchings, as well as the number of minimum dominating sets.