1. The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic
- Author
-
Wang Yi, Fan Yi-Zheng, Li Xiao-Xin, and Zhang Fei-Fei
- Subjects
unicyclic graph ,complement ,adjacency matrix ,least eigen- value ,Mathematics ,QA1-939 - 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.
- Published
- 2015
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