European Journal of Molecular & Clinical Medicine

Abstract

For a connected graph Gthe characteristic polynomial of G is the determinant value of the
matrix A(G)-λI, where A(G) is the adjacency of the matrix of G and I is the identity matrix.
The roots of the characteristic polynomial equation are known as eigen values of G. The
sum of the absolute values of the eigen values of G is called the energy of G and the largest
eigen value is the spectral radius of G. Energies of molecular graphs have various
applications in chemistry, polymerization, computer networking and pharmacy. In this
paper we present the characteristic polynomial of certain graphs in terms of recurrence
relation. Moreover we introduce a method to find the characteristic polynomial of a graph
with single vertex deletion using adjacency Rhotrix.