Note on Some New (n, m)-Type Bounds for Graph Energy

Abstract

The classical results by McClelland (1971) and Koolen & Moluton (2001) provide upper bounds for graph energy in terms of number of vertices (n) and number of edges (m). Recently, in MATCH Commun. Math. Comput. Chem. 79 (2018) and 91 (2024), new such (n, m)-type bounds were communicated. In this paper, we analyze these bounds and find that one is identical to the Koolen– Moulton bound, whereas the other is inferior to it.