A graph Gis said to be singular if its adjacency matrix is singular; otherwise, it is said to be non-singular. Non-singular trees have been completely characterized. Moreover, the singularity or non-singularity of the complement of a tree with diameter less than 5 has been completely determined. We now consider the complement  of a tree Twith diameter 5 and find the determinant of the adjacency matrix of  Furthermore, we shall determine the singularity or non-singularity of the complement of a certain class of trees with diameter 5.

adjacency matrix, complement of tree, tree with diameter 5.