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© 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 G1,ncand G2,ncbe 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 Gnc= G1,nc∪ G2,nc, a class of the connected graphs of order n whose complements are bicyclic.

Original publication

DOI

10.3390/math5010018

Type

Journal article

Journal

Mathematics

Publication Date

01/03/2017

Volume

5