Improved lower bound on the energy of line graphs

作者：Akbari, Saieed; Lin, Hongying^*

来源：Linear Algebra and Its Applications, 2023, 674: 442-452.

DOI：10.1016/j.laa.2023.05.023

• Energy
• Line graph
• Maximum degree

The energy of a graph is defined as the sum of absolute values of all eigenvalues of its adjacency matrix. For a nonempty graph G, S. Akbari, A. Alazemi, M. Andelic and M.A. Hosseinzadeh proposed a conjecture: The energy of the line graph of G is at least |E(G)| + & UDelta;(G) - 3, where E(G) is the edge set of G and & UDelta;(G) is the maximum degree of G. In this paper, we give a proof confirming the conjecture, and present a lower bound and an upper bound for the energy of line graphs of regular graphs. & COPY; 2023 Elsevier Inc.