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https://www.um.edu.mt/library/oar/handle/123456789/28169
Title: | Minimal configuration trees |
Authors: | Sciriha, Irene Gutman, Ivan |
Keywords: | Eigenvalues Mathematics -- Charts, diagrams, etc. Mathematics -- Problems, exercises, etc. |
Issue Date: | 2006 |
Publisher: | Taylor & Francis |
Citation: | Sciriha, I., & Gutman, I. (2006). Minimal configuration trees. Linear and Multilinear Algebra, 54(2), 141-145. |
Abstract: | A graph is singular of nullity η if zero is an eigenvalue of its adjacency matrix with multiplicity η. If η(G)=1, then the core of G is the subgraph induced by the vertices associated with the non-zero entries of the zero-eigenvector. A connected subgraph of G with the least number of vertices and edges, that has nullity one and the same core as G, is called a minimal configuration. A subdivision of a graph G is obtained by inserting a vertex on every edge of G. We review various properties of minimal configurations. In particular, we show that a minimal configuration is a tree if and only if it is a subdivision of some other tree. |
URI: | https://www.um.edu.mt/library/oar//handle/123456789/28169 |
Appears in Collections: | Scholarly Works - FacSciMat |
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