The Normalized Distance Laplacian by Carolyn Reinhart, Iowa State University, Class of 1960s Speaker, Friday, November 22, 1 – 1:45 pm, Stetson Court Classroom 105, Faculty Colloquium
Abstract: Spectral graph theory is the study of the properties of a graph in relation to the properties of specific associated matrices. The normalized Laplacian, which was popularized by Fang Chung in her book Spectral Graph Theory, is one such matrix and it has applications in the study of random walks. The new matrix the normalized distance Laplacian is defined analogously to the normalized Laplacian matrix. The connection between these two matrices will be explored and results on the normalized distance Laplacian will be presented, such as bounds on the eigenvalues and examples of non-isomorphic graphs with the same multiset of eigenvalues.