Algebraic Graph Theory Seminar - Cathy Wang

Title: Matching Interval Graphs

Abstract:

We consider matching integral graphs, which are graphs whose matching polynomial have only integral roots. A recent paper by Akbari, Csikvari, Ghafari, Ghezelahman, and Nahvi proved several interesting results about matching integral graphs, including characterizing all connected matching integral traceable graphs, connected matching integral claw-free graphs, matching integral regular graphs, and matching integral graphs with perfect matchings. We will take a closer look at these results.