Inertia and distance energy of line graphs of unicyclic graphs.

Abstract Let D denote the distance matrix of a connected graph. 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. The D -energy is the sum of the absolute eigenvalues of D. In this paper, we first obtain the inertia and a formula for the determinant of the distance matrices of the line graphs of unicyclic graphs; Then, as applications, we obtain the graphs with maximum (resp. minimum) D -energy among all these graphs. [ABSTRACT FROM AUTHOR]