Separation index of a graph

The concepts of separation index of a graph and of a surface are introduced. We prove that the separation index of the sphere is 3. Also the separation index of any graph faithfully embedded in a surface of genus g is bounded by a funtion of g. 2002 Wiley Periodicals, Inc. J Graph Theory 41: 53–61, 2002 1. GRAPH ISOMORPHISM This first section on the Graph Isomorphism Problem is meant only as motivation for the concept of separation index, which is defined formally in Section 2. In Section 3 we prove that the separation index of the sphere is 3. The separation index of faithfully embedded graphs is discussed in Section 4, and a few open questions are posed. The literature on the Graph Isomorphism Problem is extensive, but we have mentioned just a few references below. The Graph Isomorphism Problem is to determine, given two graphs, whether they are isomorphic. Graph Isomorphism