The inertia of distance matrices of some graphs

Let D denote the distance matrix of a connected graph G . The inertia of D is the triple of integers ( n + ( D ) , n 0 ( D ) , n − ( D ) ) , where n + ( D ) , n 0 ( D ) , n − ( D ) denote the number of positive, 0, and negative eigenvalues of D , respectively. In this paper, we mainly give some graphs whose n + ( D ) is equal to 1 and get the inertia of their distance matrices.