A graph G of order n is borderenergetic if it has the same energy as the complete graph K n . In this paper, we obtain the result that for any connected graph G, except for the five graphs (one of order 5, three of order 6 and one of order 10), the line graph L(G) of G is not borderenergetic. As a consequence, we get that if G is a borderenergetic graph, then the line graph L(G) of G is not borderenergetic. In addition, we observe a relation between the lower bound of the energy of the line graph L(G) of a borderenergetic graph G and the minimum degree δ(G) of G.

The classical graph entropy based on the vertex coloring proposed by Mowshowitz depends on a graph. In fact, a hypergraph, as a generalization of a graph, can express complex and high-order relations such that it is often used to model complex systems. Being different from the classical graph entropy, we extend this concept to a hypergraph. Then, we define the graph entropy based on the vertex strong coloring of a hypergraph. Moreover, some tightly upper and lower bounds of such graph entropies as well as the corresponding extremal hypergraphs are obtained.