关于图的同构不动边

ON THE FIXED EDGE OF GRAPHS

图G的一条边e称为G的同构不动边,如果G—e+e’≌G当且仅当e’=e.若e=uv是G的同构不动边,那么对G—e的任意自同构映射π有π({u,v})={u,v}.图的同构不动边反映了二元关系系统中的定性关系,改变这种关系将改变系统的结构.这种关系的存在对系统的重构有重要的意义.本文中猜想:几乎所有的图含同构不动边.为支持这个猜想,列出了所有不含同构不动边的树形图和单圈图.

An edge e of graph G=(V(G), E(G)) is called an isomorphism fixed edge if G-e+e'■G implies that e'=e. The isomorphism fixed edge representes a key relation of relation system, if the key relation is changed the structure of the system will be changed, and it plays an important role in the edge reconstruction of graphs. We conjectured that almost all graphs have isomorphism fixed edge. To support this conjecture, we list all trees and unicycle graphs whict do not contain isomorphism fixed edge.