UPPER BOUND FOR EXPANSION RATE IN FINITE AND CONNECTED GRAPH - Aziez Rachmansyah, Kemal
Expansion rate in finite and connected graph for a set of vertices is the least integer of the number of edges so that the neighborhood around that set of vertices have at least half the graphs weight. This study is intended to find the upper bound expansion rate which depends only on the graph and the set of vertices. Eigenvalues of the Laplace operator is used as main tool. Two upper bounds are obtained and one of them is relatively close to the actual expansion rate. Examples for some graphs are given to see the closeness between the upper bounds and the expansion rate. This study is a rewriting, elaboration, and simulation of proofs by Fan R.K. Chung et al. (1997) dan Grigor’yan (2019).