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7554634 
Journal Article 
(Laplacian) Borderenergetic Graphs and Bipartite Graphs 
Deng, B; Li, XL; Zhao, HX 
2019 
1 
Match (Mülheim an der Ruhr, Germany)
ISSN: 0340-6253 
82 
2 
481-489 
WOS:000491305000009 
A graph G of order n and size m is (Laplacian) borderenergetic if it has the same (Laplacian) energy as the complete graph K-n does. In this paper, we prove that when m < 2(n-1)(2)/n, a borderenergetic graph is not bipartite. Moreover, for a borderenergetic bipartite graph, we present a lower bound of its largest eigenvalue and an upper bound of its middle eigenvalue, respectively. Analogously, Laplacian borderenergetic bipartite graphs is observed and some asymptotically tight bounds on their first Zagreb indices are shown.