Abstract

Let β H denote the orbit graph of a finite group H . Let ζ 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 ζ , and two vertices in ζ 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 .

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