COMPLEMENTARY DISTANCE SPECTRA AND COMPLEMENTARY DISTANCE ENERGY OF LINE GRAPHS OF REGULAR GRAPHS - Ramane, Harishchandra S.; Nandeesh, K.C. (IndoMS, 2016)
The complementary distance (CD) matrix of a graph G is defined as CD(G) = [c_ij], where c_ij = 1+D-d_ij if i ≠ j and c_ij = 0, otherwise, where D is the diameter of G and d_ij is the distance between the vertices v_i and v_j in G. The CD-energy of G is defined as the sum of the absolute values of the eigenvalues of CD-matrix. Two graphs are said to be CD-equienergetic if they have same CD-energy. In this paper we show that the complement of the line graph of certain regular graphs has exactly one positive CD-eigenvalue. Further we obtain the CD-energy of line graphs of certain regualr graphs and thus constructs pairs of CD-equienergetic graphs of same order and having different CD-eigenvalues.DOI :Â http://dx.doi.org/10.22342/jims.22.1.205.27-35