Speaker
Mr
Matt Burnham
(Iowa State University)
Description
Given a real number $q$, the $q$-Laplacian of a graph $G$ is the matrix $A+qD$ where $A$ is the adjacency matrix and $D$ the diagonal degree matrix. If the edge set of $G$ can be partitioned into edge-disjoint copies of $K_t$, then $G$ is called $K_{t}$-decomposable.
In this talk, we generalize some results from a survey paper of Cvetković, Rowlinson, and Simić about the signless Laplacian $A+D$ to the $\frac{1}{t-1}$-Laplacian of $K_t$-decomposable graphs. In particular, we generalize the correspondence between the signless Laplacian and line graphs, positive semi-definiteness, and characterization of graphs with a zero eigenvalue.
Author
Mr
Matt Burnham
(Iowa State University)
Co-author
Prof.
Steve Butler
(Iowa State University)