  The energy of a graph is defined as the sum the absolute values of the
eigenvalues of its adjacency matrix. A graph G on n vertices is said to be
borderenergetic if its energy equals the energy of the complete graph Kn. In
this paper, we promote this concept for the Laplacian matrix, introduced by
Gutman and Zhou [5]. We say G to be L-borderenergetic if LE(G) = LE(Kn).
Several classes of L-borderenergetic graphs are obtained including result that
for each positive integer r; there are 2r +1 graphs, of order n = 4r + 4;
pairwise L-noncospectral and L-bordernergetic graphs.
