Abstract
The graph \(G\) of order \(n\) is an L-borderenergetic graph which means it has the same Laplacian energy as the complete graph \(K_{n}\). In this paper, we find that the combination of complete bipartite 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 the structural characteristics of L-borderenergetic graphs.
