On the Spectra of Principal Ideal Graph of Completely Simple Semigroups
Sijo George
Department of Mathematics, University College, Thiruvananthapuram, Kerala-695034, India.
R S Indu
Department of Mathematics, University College, Thiruvananthapuram, Kerala-695034, India.
C S Preenu *
Department of Mathematics, University College, Thiruvananthapuram, Kerala-695034, India.
K R Santhoshkumar
Department of Mathematics, University College, Thiruvananthapuram, Kerala-695034, India.
*Author to whom correspondence should be addressed.
Abstract
Consider T to be a semigroup. The principal left(right) ideal graph PiGℒ (PiGℛ) is defined by taking the elements of T as vertices, with two elements being adjacent whenever their principal left (right) ideals intersect. We focus on the case of completely simple semigroups and compute various graph energies, including adjacency energy (Ad-energy), signless Laplacian energy (Sl-energy), and Laplacian energy (Lp-energy). Further, the interrelations among these energies are established.
Keywords: Principal ideal graphs, adjacency energy, laplacian energy, signless Laplacian energy, completely simple semigroup