THE VERTEX DISTANCE COMPLEMENT SPECTRUM OF SUBDIVISION VERTEX JOIN AND SUBDIVISION EDGE JOIN OF TWO REGULAR GRAPHS

The vertex distance complement (VDC) matrix \(\textit{C}\), of a connected graph \(G\) with set consisting \(n\) vertices, is real symmetric \([c_{ij}]\) that takes the value \(n - d_{ij}\) where \(d_{ij}\) between vertices \(v_i\) and \(v_j\) for \(i \neq j\) 0 otherwise. spectrum subdivision join, \(G_1 \dot{\bigvee} G_2\) edge join \underline{\bigvee} regular graphs \(G_1\) \(G_2\) in terms adjacency are determined this paper.