The graph G of order n is an L-borderenergetic graph which means it has the same Laplacian energy as the complete graph Kn. In this paper, we find that the combination of complete bi-partite graphs and stars can construct infinite numbers of infinite classes L-borderenergetic graphs. We give two infinite numbers of infinite classes L-borderenergetic graphs and two infinite classes L-borderenergetic graphs under the operators union, join and their mixed. This research could provide experience for further study...
