Characteristic Polynomial and Energy of Matrices Associated with Power Graphs of Cyclic Groups

Abstract

Algebraic graph theory is a fast-expanding field with numerous applications, particularly in the study of power graphs of finite groups. This study focuses on the power graph of cyclic groups with prime power order. Several key results are presented, including the characteristic polynomial and the energies of different matrices associated with the power graph. These matrices include the degree sum, degree exponent, degree subtraction, maximum degree, and degree square sum matrix. The research establishes characteristic polynomial for each matrix and computes their respective energies, revealing the complex relationships between the structure of the graph and its algebraic properties. This work extends the understanding of power graphs and contributes valuable insights into their algebraic and spectral properties.