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- Title
Universal adjacency spectrum of the commuting and non-commuting graphs on AC-groups.
- Authors
Bajaj, Saraswati; Panigrahi, Pratima
- Abstract
For a simple undirected graph H and α , β , γ , η ∈ ℝ , α ≠ 0 , the universal adjacency matrix U (H) = α A (H) + β D (H) + γ I + η J , where I is the identity matrix, J is the all-ones matrix, and A (H) and D (H) are the adjacency and degree diagonal matrices of H , respectively. For a finite non-abelian group G and Ω ⊆ G , the commuting graph Δ (G , Ω) is a simple undirected graph with vertex set Ω and the adjacency rule is commuting. The non-commuting graph of G is the complement of Δ (G , Ω). An AC-group is a non-abelian group such that the centralizer of every non-central element is abelian. In this paper, we obtain the universal adjacency eigenpairs of the commuting and non-commuting graphs for an arbitrary AC-group G with Ω = G or G − Z (G). Moreover, we determine the eigenpairs of U (Δ (G , Ω)) when G is a specific kind of group.
- Subjects
NONABELIAN groups; COMMUTING; FINITE groups; UNDIRECTED graphs; CAYLEY graphs; FINITE simple groups
- Publication
Asian-European Journal of Mathematics, 2024, Vol 17, Issue 1, p1
- ISSN
1793-5571
- Publication type
Article
- DOI
10.1142/S1793557123502376