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A  c -cyclic graph is a connected graph with  n  vertices and  n  +  c −1 edges. In this paper, we consider the problem that: in the class of graphs, each of which is the complement graph of a  c -cyclic graph with  n  vertices, which graph has the largest-spectral radius. We shall show that, for, the extremal graph must be a graph with an isolated vertex. This implies that the maximum degree of  G  is larger, then the-spectral radius of its complement graph is also larger. We also determine the structure of the extremal graph with largest-spectral radius among the class of graphs, each of which is the complement graph of a  c -cyclic graph with  n  vertices and maximum degree  n −1 forand  n −2 for, respectively.

The A α -spectral radius of dense graphs