2022/10/03 by Yogendra Singh, Singh, Yogendra, Anand Kumar Tiwari +3
Computer Science · Engineering · Mathematics · #05C12 #05C25 #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Spectral Theory (math.SP) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2210.00709
openalex publication_date 2022/10/03 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
The power graph G = P(Ω) of a finite group Ω is a graph with the vertex set Ω and two vertices u, v ∈ Ω form an edge if and only if one is an integral power of the other. Let D(G), A(G), RT(G), and RD(G) denote the degree diagonal matrix, adjacency matrix, the diagonal matrix of the vertex reciprocal transmission, and Harary matrix of the power graph G respectively. Then the Aα and RDα matrices of G are defined as Aα(G) = αD(G) + (1-α)A(G) and RDα(G) = αRT(G) + (1-α)RD(G). In this article, we determine the eigenvalues of Aα and RDα matrices of the power graph of group G = ⟨ s,r : r2kp = s2 = e,~ srs-1 = r^2k-1p-1⟩. In addition, we calculate its distant and detotar distance degree sequences, metric dimension, and strong metric dimension.