Characterization of the minimizing graph of the connected graphs whose complements are bicyclic
© 2017 by the authors. 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. Let G 1,n c and G 2,n c be 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 to G n c = G 1,n c ∪ G 2,n c , a class of the connected graphs of order n whose complements are bicyclic.