On the Laplacian energy of an orbit graph of finite groups. (English) Zbl 1541.05103
Summary: Let \(\beta_H\) denote the orbit graph of a finite group \(H\). Let \(\zeta\) be the set of commuting elements in \(H\) with order two. An orbit graph is a simple undirected graph where non-central orbits are represented as vertices in \(\zeta \), and two vertices in \(\zeta\) are connected by an edge if they are conjugate. In this article, we explore the Laplacian energy and signless Laplacian energy of orbit graphs associated with dihedral groups of order \(2w\) and quaternion groups of order \(2^w\).
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
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