The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic
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 suc...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2015-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.1796 |
| Summary: | 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. |
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| ISSN: | 2083-5892 |