| Popis: |
The matching energy of a graph G , denoted by M E ( G ) , is defined as the sum of absolute values of the zeros of the matching polynomial of G . In this paper, we would like to present some lower bounds for M E ( G ) . For any connected graph G , it is proved that M E ( G ) ≥ 2 μ ( G ) , where μ ( G ) is the matching number of G . Also it is shown that if G has no perfect matching, then M E ( G ) ≥ 2 μ ( G ) + 1 , except for K 1 , 2 . We characterize some class of graphs whose matching energy is at least equal to the number of vertices. It is shown that if G is a connected graph of order n , such that the multiplicity of 0 as a matching root is 1, then M E ( G ) > n , except for K 1 , 2 . Also, it is proved that in a connected graph G of order n , if the multiplicity of 0 as a matching root is 2, then M E ( G ) > n with only four exceptions. |
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