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Minimal configuration unicyclic graphs.
- Source :
-
Linear & Multilinear Algebra . Jan2009, Vol. 57 Issue 1, p19-27. 9p. 4 Diagrams. - Publication Year :
- 2009
-
Abstract
- A graph G is singular with nullity η(G), if zero is an eigenvalue of its adjacency matrix with multiplicity η(G). If η(G) = 1, then the core of G is the subgraph induced by the vertices associated with the non-zero entries of the kernel eigenvector. The set of vertices which are not in the core is called the periphery of G. A graph G with nullity one is called a minimal configuration if no two vertices in the periphery are adjacent and deletion of any vertex in the periphery increases the nullity. In this article, we describe the structure of a singular unicyclic graph and single out the class of unicyclic graphs which are minimal configurations. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03081087
- Volume :
- 57
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Linear & Multilinear Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 34783185
- Full Text :
- https://doi.org/10.1080/03081080701483081