2024/11/27 by Priti Prasanna Mondal, Mondal, Priti Prasanna, Basit Auyoob Mir +3
Computer Science · Mathematics · #FOS: Mathematics #Finite Group Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2411.18244
openalex publication_date 2024/11/27 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28
Consider a group \mathbbG and construct its power graph, whose vertex set consists of the elements of \mathbbG. Two distinct vertices (elements) are adjacent in the graph if and only if one element can be expressed as an integral power of the other. In this article, we improved the bounds of the spectral radius of the power graphs of the cyclic group Cn, the dihedral group D2n, and the dicyclic group Q4n. For n≠ pm, the power graph of the cyclic group Cn is not a complete multipartite graph. We find the second largest eigenvalue bounds of the same with the clique number. In some cases, we find the bounds are exact if and only if they belong to a particular family of graphs. Lastly, we work on the distance spectral radius of the power graphs of the same groups