TY - JOUR
AU - Gohdar Mohiaddin
AU - Khidir Sharaf
PY - 2019/10/30
Y2 - 2020/02/22
TI - Null Spaces Dimension of the Eigenvalue -1 in a Graph
JF - Science Journal of University of Zakho
JA - sjuoz
VL - 7
IS - 4
SE - Science Journal of University of Zakho
DO - 10.25271/sjuoz.2019.7.4.609
UR - https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/609
AB - 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.
ER -