摘要 : We consider the symmetric difference of two graphs on the same vertex set [n], which is the graph on [n] whose edge set consists of all edges that belong to exactly one of the two graphs. Let .F be a class of graphs, and let M\scr... 展开 We consider the symmetric difference of two graphs on the same vertex set [n], which is the graph on [n] whose edge set consists of all edges that belong to exactly one of the two graphs. Let .F be a class of graphs, and let M\scrF (n) denote the maximum possible cardinality of a family c of graphs on [n] such that the symmetric difference of any two members in c belongs to .F. These 379--403] with the aim of providing a new graphic approach to coding theory. In particular, M\scrF (n) denotes the maximum possible size of this code. Existing results show that as the graph class .F changes, M\scrF (n) can vary from n to 2(1+o(1)) 2. We study several phase transition problems related to M\scrF (n) in general settings and present a partial solution to a recent problem posed by Alon et al. 收起