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Research Paper | Mathematics | India | Volume 11 Issue 3, March 2022

On Conjugate Graphs of Dihedral Group

Chinmayee Kumar ^[2] | Kuntala Patra ^[3]

Abstract: 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.

Keywords: Conjugate graph, Dihedral Group, Line Graph, Energy

Edition: Volume 11 Issue 3, March 2022,

Pages: 227 - 231