On Conjugate Graphs of Dihedral Group

The conjugate graph ?_C^G (G) of a non-abelian group G is a graph whose vertices are the elements of G and two vertices are adjacent if they belong to the same conjugacy class. In this paper, we study the line graphs and complement of conjugate graphs of D_n and explore graph properties like chromatic number, independence number, diameter, planarity, vertex and edge connectivity. Further, results related to the spectrum and energy of line graphs have also been discussed.