ABSTRACT:A method for construction of the characteristic polynomial (CP) coefficients of the three classes of reciprocal graphs, viz., L n ϩ n( p), C n ϩ n( p), and K 1,nϪ1 ϩ n( p), has been developed that requires only the value of n. The working formulas have been expressed in matrix product form, computer programs for which can easily be developed.