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What is a subgraph? We go over it in today's math lesson! If you're familiar with subsets, then subgraphs are probably exactly what you think they are. Recall that a graph G = (V(G), E(G)) is an ordered pair with a vertex set V(G) and an edge set E(G). Then, another graph H = (V(H), E(H)) is a subgraph of G if and only if V(H) is a subset of V(G) and E(H) is a subset of E(G). So, a graph H is a subgraph of G if and only if every vertex and edge in H is also in G. Thus, just like with subsets, every subgraph is a subgraph of itself. If a graph H is a subgraph of G, and H is not equal to G, we say H is a proper subgraph of G.

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