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Today were going to explore signed graphs. Well look at the definition and basic properties of signed graphs, and then well move on to the concept of a balanced signed graph, the switching operation, the concept of frustration, and finally, well look at an application of signed graphs. A signed graph (G, sigma) is an unsigned graph G with vertex set V(G) and edge set E(G), together with a function sigma, known as our graphs signature, which assigns to each edge a positive or negative sign. Basically, a signed graph is just a graph whose edges have positive or negative signs. Just like we have subgraphs of unsigned graphs, we can also have subgraphs of signed graphs. A subgraph of a signed graph (G, sigma) is another signed graph, (H, sigmae(H)) whose underlying graph H is a subgraph in the usual sense of the underlying graph G of our original signed graph, and where the signs on any edge in (H ,sigmae(H)) are the same as on that edge in the origi