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| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Sciriha, Irene | - |
| dc.date.accessioned | 2018-03-27T06:51:21Z | - |
| dc.date.available | 2018-03-27T06:51:21Z | - |
| dc.date.issued | 1999 | - |
| dc.identifier.citation | Sciriha I. (1999). On the rank of graphs. In Y. Alavi, D. R. Lick & A. Schwenk (Eds.), Graph theory and algorithms II (pp. 769-778). Michigan: Springer. | en_GB |
| dc.identifier.uri | https://www.um.edu.mt/library/oar//handle/123456789/28350 | - |
| dc.description.abstract | The properties of singular graphs obtained in a previous paper "On the construction of graphs of nullity one", lead to the characterization of graphs of small rank. The minimal conßgurations that are contained in singular graphs were identißed as "grown" from certain cores. A core of a singular graph G is a subgraph induced by the vertices corresponding to the non-zero components of an eigenvector in the nullspace of the adjacency matrix of G. In this paper it is shown that an arbitrary singular graph Z without isolated vertices has core-sizes corresponding to a minimal basis for the nullspace of A bounded below by 2 and above by r(Z) + 1, r(Z) being the rank of Z. For r(Z) greater or equal to 6, these bounds are sharp. | en_GB |
| dc.language.iso | en | en_GB |
| dc.publisher | Springer | en_GB |
| dc.rights | info:eu-repo/semantics/restrictedAccess | en_GB |
| dc.subject | Mathematics -- Charts, diagrams, etc. | en_GB |
| dc.subject | Mathematics -- Problems, exercises, etc. | en_GB |
| dc.title | On the rank of graphs | en_GB |
| dc.title.alternative | Graph theory and algorithms II | en_GB |
| dc.type | bookPart | en_GB |
| dc.rights.holder | The copyright of this work belongs to the author(s)/publisher. The rights of this work are as defined by the appropriate Copyright Legislation or as modified by any successive legislation. Users may access this work and can make use of the information contained in accordance with the Copyright Legislation provided that the author must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the prior permission of the copyright holder. | en_GB |
| dc.description.reviewed | peer-reviewed | en_GB |
| Appears in Collections: | Scholarly Works - FacSciMat | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| On_the_Rank_of_Graphs_1999.pdf Restricted Access | 1.11 MB | Adobe PDF | View/Open Request a copy |
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