LAUSR

Abstract The energy E ( G ) of a graph G is the sum of the absolute values of all eigenvalues of G . We are interested in the relation between the energy of a graph G and the matching number μ ( G ) of G . It is proved that E ( G ) ≥ 2 μ ( G ) for every graph G , and E ( G ) ≥ 2 μ ( G ) + 5 5 c 1 ( G ) if the cycles of G (if any) are pairwise vertex-disjoint, where c 1 ( G ) denotes the number of odd cycles in G . Besides, we prove that E ( G ) ≥ r ( G ) + 1 2 if G has at least one odd cycle and it is not of full rank, where r ( G ) is the rank of G .