Characteristic polynomial of maximum and minimum matrix of square power graph of dihedral group of order 2n with odd natural number n

Abstract

For dihedral group Dn of order 2n with identity element R0, Square power graph of dihedral group Dn is an undirected finite, simple graph having pair of distinct vertices X1,X2 have edge iff X1 X2 = X2 or X2 X1 = X2 for any X ∈ Dn where X2 ≠ R0. In this research, we have calculated characteristic polynomials of degree of vertex based matrices such as maximum and minimum matrix of the Square power graph of dihedral group Dn of order 2n with odd natural number n.