Abstract

A graph G is C-MH-homogeneous, or C-MH, if every monomorphism between finite connected induced subgraphs of G extends to a homomorphism from G into itself. Similarly, G is C-IH if every isomorphism between finite connected induced subgraphs of G extends to a homomorphism from G into itself. In this paper, the finite C-MH graphs are characterized and a new family of finite C-IH graphs is discussed.

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