On spectrum and energies of enhanced power graphs - Pankaj Kalita; Prohelika Das (Mathematics Open, 2025)
The enhanced power graph [Formula: see text] of a group G is a simple graph with vertex set G and two distinct vertex are adjacent if and only if they belong to the same cyclic subgroup. In this paper, we present the characteristic polynomial of adjacency matrix, Laplacian matrix, and signless Laplacian matrix of enhanced power graphs of some groups such as dihedral group [Formula: see text], di-cyclic group [Formula: see text] and semi-dihedral group [Formula: see text]. Also, we find the Laplacian energy of those enhanced power graphs. We prove that the enhanced power graphs of these groups are L-hyperenergetic.