What is a Spanning Subgraph? | Graph Theory

What is a spanning subgraph? We go over this special type of subgraph in today's math lesson! Recall that a graph is an ordered pair G = ( V(G), E(G) ) with vertex set V and edge set E. 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). Basically, this means H is a subgraph of G if everything in H is also in G. Then, H is a spanning subgraph of G if and only if V(H) = V(G). In other words, H is a spanning subgraph of G if H is a subgraph of G, and H has the same vertex set as G. The graph H 'spans' the vertex set of G and has some or all of the edges in G. Also, remember that H has no edges not in G. So one last time, H is a spanning subgraph of G if and only if H is a subgraph of G, and the vertex set of H is equal to the vertex set of G.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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