A lower bound for graph energy

ABSTRACT

The energy $\mathcal{E}\left(G\right)$ of a graph G is the sum of the absolute values of all eigenvalues of G. More recently, the authors of Wong, Wang and Chu [Lower bounds of graph energy in terms of matching number. Linear Algebra Appl. 2018;549:276–286] obtained a lower bound for graph energy. They proved that, for a connected graph G apart from $K_1,K_3$ and $K_{p,q}$ with $1\le pq\le 4$, the energy of G is at least $2\sqrt{5}$. In the present paper, we aim to improve the lower bound from $2\sqrt{5}$ to 6. The extreme graphs with energy 6 are characterized.

KEYWORDS:

• Graph energy
• rank
• matching number

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 05C20
• 05C50
• 05C75

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work for the author Dein Wong was supported by the Fundamental Research Funds for the Central Universities (no. 2018ZDPY06).