RELATIONSHIPS BETWEEN THE METRIC DIMENSION AND SPECTRUM OF GRAPHS - Farhan, Mohammad
The algebraic approach to graph theoretical problems has been extensively studied by looking at the spectrum of a graph’s matrix representation. In this thesis, we investigate some relationships between the metric dimension of a graph G and its nullity, that is, the multiplicity of eigenvalue 0 of the adjacency matrix of G, and the eigenvalues of its Laplacian and distance matrices. Furthermore, we also present a relationship between the metric dimension of a graph and its nullity, using twin classes.