Isoperimetric numbers of graph bundles

Abstract

The main aim of this paper is to give some upper and lower bounds for the isoperimetric numbers of graph coverings or graph bundles, with exact values in some special cases. In addition, we show that the isoperimetric number of any covering graph is not greater than that of the base graph. Mohar's theorem for the isoperimetric number of the cartesian product of a graph and a complete graph can be extended to a more general case: The isoperimetric number i(G x K-2n) of the cartesian product of any graph G and a complete graph K-2n on even vertices is the minimum of the isoperimetric number i(G) and n, and it is also a sharp lower bound of the isoperimetric numbers of all graph bundles over the graph G with fiber K-2n. Furthermore, if n greater than or equal to 2i(G) then the isoperimetric number of any graph bundle over G with fibre K-n is equal to the isoperimetric number i(G) of G.