The Energy of Conjugate Graph of Some Finite Metabelian Groups of Order Less Than 24

The conjugacy classes of the Metabelian group G, plays an important role in defining the conjugate graph, whose vertices are non-central elements of G, and two vertices are connected if and only if they are conjugate. The constructions of conjugate graphs of all non abelian metabelian groups of order less than 24 are the basis for this paper. And the obtained results are then used to calculate the energy of the aforementioned group. This is aided by specialized programming software (maple).