Abstract
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 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 Lborderenergetic graphs under the operators union, join and their mixed. This research could provide experience for further study the structural characteristics of L-borderenergetic graphs.
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