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In a certain class of graphs, a graph is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. LetG  1 , n  candG  2 , n  cbe the classes of the connected graphs of order n whose complements are bicyclic with exactly two and three cycles, respectively. In this paper, we characterize the unique minimizing graph among all the graphs which belong toG n c  =  G  1 , n  c  ∪  G  2 , n  c, a class of the connected graphs of order n whose complements are bicyclic

Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic