Congressus Numerantium, 131 (1998), pp. 135-143.
Ömer Egecioglu and Cemil M. Azizoglu
Isoperimetric Number of the Cartesian Product of Graphs and Paths
Abstract.
We prove that the isoperimetric number of P_k x G_k,
the Cartesian product of the path P_k and a connected graph with k
vertices, is equal to the isoperimetric number of P_k itself.
At the same time
we construct an infinite family of graphs that
shows that this is not true for P_k x G where
G has more than k vertices, even if G is a tree.
omer@cs.ucsb.edu