Some Observations on the Smallest Adjacency Eigenvalue of a Graph
In this paper, we discuss various connections between the smallest eigenvalue of the adjacency matrix of a graph and its structure. There are several techniques for obtaining upper bounds on the smallest eigenvalue, and some of them are based on Rayleigh quotients, Cauchy interlacing using induced s...
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| Veröffentlicht in: | Discussiones Mathematicae. Graph Theory 2020-05, Vol.40 (2), p.467-493 |
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| container_title | Discussiones Mathematicae. Graph Theory |
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| creator | Cioabă, Sebastian M. Elzinga, Randall J. Gregory, David A. |
| description | In this paper, we discuss various connections between the smallest eigenvalue of the adjacency matrix of a graph and its structure. There are several techniques for obtaining upper bounds on the smallest eigenvalue, and some of them are based on Rayleigh quotients, Cauchy interlacing using induced subgraphs, and Haemers interlacing with vertex partitions and quotient matrices. In this paper, we are interested in obtaining lower bounds for the smallest eigenvalue. Motivated by results on line graphs and generalized line graphs, we show how graph decompositions can be used to obtain such lower bounds. |
| doi_str_mv | 10.7151/dmgt.2285 |
| format | Article |
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| issn | 1234-3099 2083-5892 |
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| source | DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | 05C50 05C75 05C76 05E30 15A18 adjacency matrix claw-free graphs clique partition graph decomposition graph spectrum maximum cut smallest eigenvalue |
| title | Some Observations on the Smallest Adjacency Eigenvalue of a Graph |
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