Constructions for cospectral graphs for the normalized Laplacian matrix and distance matrix
Is Version Of
In discrete mathematics, a graph is a representation of relationships between objects. Using linear algebraic techniques, we can encode a graph into a matrix. However, as the graph grows, so too does the matrix. This leads to computational limitations and necessitates the development of techniques to capture a portion of the graph's structure. Spectral graph theory is one such method, which looks at the eigenvalues (or spectrum) of the matrix associated with the graph. We know only a portion of the structure is captured by the existence of cospectral graphs, or fundamentally different graphs with the same eigenvalues. Exploring cospectral graphs helps us understand which information is contained in the spectrum. In this thesis, we describe methods of creating cospectral graphs, specifically those with differing numbers of edges.