The extremal graphs with respect to their nullity
The nullity of a graph G , denoted by η ( G ) , is the multiplicity of the eigenvalue zero of its adjacency matrix. In this paper, we determine all graphs with η ( G ) = n ( G ) − 2 m ( G ) − c ( G ) , where c ( G ) = e ( G ) − n ( G ) + ω ( G ) , and n ( G ) , e ( G ) , m ( G ) , and ω ( G ) are th...
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| Veröffentlicht in: | Journal of inequalities and applications 2016-02, Vol.2016 (1), p.1-13, Article 71 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The nullity of a graph
G
, denoted by
η
(
G
)
, is the multiplicity of the eigenvalue zero of its adjacency matrix. In this paper, we determine all graphs with
η
(
G
)
=
n
(
G
)
−
2
m
(
G
)
−
c
(
G
)
, where
c
(
G
)
=
e
(
G
)
−
n
(
G
)
+
ω
(
G
)
, and
n
(
G
)
,
e
(
G
)
,
m
(
G
)
, and
ω
(
G
)
are the vertex number, edge number, matching number, and the number of connected components of
G
, respectively. |
|---|---|
| ISSN: | 1029-242X 1025-5834 1029-242X |
| DOI: | 10.1186/s13660-016-1018-z |