Subgraphs and their embeddings

If also the stronger condition y i,j]) = yilUj ) holds for each i,j e B(y ), we call y a closed subgraph of y and write 

wherever there is a bond in y, there is also a bond in y with the same multiplicity, and vice versa, wherever there is a bond in y between nodes in JV, there is also a bond in y with the same multiplicity, then y is called the N-inducedsubgraph of y, and we write 

In the next step we transfer the subgraph relations from labeled to unlabeled graphs. This is quite important since we shall speak of substructures of molecular graphs, i.e. of subgraphs of unlabeled multigraphs. 

7 Definition (Embeddings of labeled graphs) Consider y g together with a nonempty subset N of the set of (labels of) nodes, N s and y e 9m,n-An injective mapping from N to n, for short (/) g is called an embedding of y in y 

Here is a small case that illustrates the definition  

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