2014/06/30 by Cid Reyes-Bustos
Mathematics · #Bipartite graph #Cayley graph #Characteristic subgroup #Combinatorics #Discrete mathematics #Finite Group Theory Research #Graph #Graph theory and applications #Group (periodic table) #Limits and Structures in Graph Theory #Line graph #Mathematics #Normal subgroup #Ramanujan's sum #Social connectedness #Symmetric graph #Symmetric group #Voltage graph #math.CO #math.GR #msc:05C25 #msc:05C50
paper · pdf · doi:10.1016/j.laa.2015.09.049
published as Linear Algebra and its Applications 488 (2016) 320-349
arxiv created 2014/11/24 · openalex publication_date 2015/11/17 · arxiv updated 2015/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we introduce a Cayley-type graph for group-subgroup pairs and present some elementary properties of such graphs, including connectedness, their degree and partition structure, and vertex-transitivity. We relate these properties to those of the underlying group-subgroup pair. From the properties of the group, subgroup and generating set some of the eigenvalues can be determined, including the largest eigenvalue of the graph. In particular, when this construction results in a bipartite regular graph we show a sufficient condition on the size of the generating sets that results on Ramanujan graphs for a fixed group-subgroup pair. Examples of Ramanujan pair-graphs that do not satisfy this condition are also provided, to show that the condition is not necessary.