A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and contains exactly one cycle (namely the class Ucn of graphs whose complements are unicyclic), and characterize the unique minimizing graph in Ucn when n ≥ 20.
@article{bwmeta1.element.doi-10_7151_dmgt_1796,
author = {Yi Wang and Yi-Zheng Fan and Xiao-Xin Li and Fei-Fei Zhang},
title = {The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {249-260},
zbl = {1311.05119},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1796}
}
Yi Wang; Yi-Zheng Fan; Xiao-Xin Li; Fei-Fei Zhang. The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 249-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1796/
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