Null Spaces Dimension of the Eigenvalue -1 in a Graph
| Autor: | Gohdar H. Mohiaddin, Khidir R. Sharaf |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Science Journal of University of Zakho, Vol 7, Iss 4 (2019) |
| Druh dokumentu: | article |
| ISSN: | 2663-628X 2663-6298 |
| DOI: | 10.25271/sjuoz.2019.7.4.609 |
| Popis: | In geographic, the eigenvalues and eigenvectors of transportation network provides many informations about its connectedness. It is proven that the more highly connected in a transportation network G has largest eigenvalue and hence more multiple occurrences of the eigenvalue -1. For a graph G with adjacency matrix A, the multiplicity of the eigenvalue -1 equals the dimension of the null space of the matrix A + I. In this paper, we constructed a high closed zero sum weighting of G and by which its proved that, the dimension of the null space of the eigenvalue -1 is the same as the number of independent variables used in a non-trivial high closed zero sum weighting of the graph. Multiplicity of -1 as an eigenvalue of known graphs and of corona product of certain classes of graphs are determined and two classes of -1- nut graphs are constructed. |
| Databáze: | Directory of Open Access Journals |
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