# The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic

Yi Wang; Yi-Zheng Fan; Xiao-Xin Li; Fei-Fei Zhang

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 2, page 249-260
- ISSN: 2083-5892

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topYi Wang, et al. "The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic." Discussiones Mathematicae Graph Theory 35.2 (2015): 249-260. <http://eudml.org/doc/271086>.

@article{YiWang2015,

abstract = {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.},

author = {Yi Wang, Yi-Zheng Fan, Xiao-Xin Li, Fei-Fei Zhang},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {unicyclic graph; complement; adjacency matrix; least eigen- value; least eigenvalue},

language = {eng},

number = {2},

pages = {249-260},

title = {The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic},

url = {http://eudml.org/doc/271086},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Yi Wang

AU - Yi-Zheng Fan

AU - Xiao-Xin Li

AU - Fei-Fei Zhang

TI - The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 2

SP - 249

EP - 260

AB - 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.

LA - eng

KW - unicyclic graph; complement; adjacency matrix; least eigen- value; least eigenvalue

UR - http://eudml.org/doc/271086

ER -

## References

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