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jack_bauer
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I'm wondering, is it possible a graph G and its complement G' to be complete?
jack_bauer said:I'm wondering, is it possible a graph G and its complement G' to be complete?
The complement of a graph is a new graph that contains all the same vertices as the original graph, but the edges are reversed. In other words, if two vertices in the original graph are connected by an edge, they will not be connected in the complement graph, and vice versa.
The complement of a graph can be represented either as a list of edges or as an adjacency matrix. In both cases, the complement graph will have the same number of vertices as the original graph, but the connections will be reversed.
The complement of a graph is useful in a variety of applications, including network analysis, graph coloring, and circuit design. It can also help identify patterns or relationships within a graph that may not be as easily visible in the original graph.
The complement of a graph can be calculated using a simple formula where the number of edges in the complement graph is equal to the number of possible edges minus the number of edges in the original graph. For example, if the original graph has 5 vertices and 8 edges, the complement graph will have 5 vertices and (5*4)/2 - 8 = 2 edges.
Yes, a self-complementary graph is a graph that is isomorphic to its own complement. In other words, the complement of a self-complementary graph is identical to the original graph. There are also graphs that do not have a complement, such as null graphs (graphs with no edges) and complete graphs (graphs where every pair of vertices is connected by an edge).