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Bounds for the positive and negative inertia index of a graph.
- Source :
-
Linear Algebra & its Applications . Jun2017, Vol. 522, p15-27. 13p. - Publication Year :
- 2017
-
Abstract
- Let G be a graph and let A ( G ) be adjacency matrix of G . The positive inertia index (respectively, the negative inertia index) of G , denoted by p ( G ) (respectively, n ( G ) ), is defined to be the number of positive eigenvalues (respectively, negative eigenvalues) of A ( G ) . In this paper, we present the bounds for p ( G ) and n ( G ) as follows: m ( G ) − c ( G ) ≤ p ( G ) ≤ m ( G ) + c ( G ) , m ( G ) − c ( G ) ≤ n ( G ) ≤ m ( G ) + c ( G ) , where m ( G ) and c ( G ) are respectively the matching number and the cyclomatic number of G . Furthermore, we characterize the graphs which attain the upper bounds and the lower bounds respectively. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 522
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 121755939
- Full Text :
- https://doi.org/10.1016/j.laa.2017.02.005