More explanation: The adjacency matrix of a disconnected graph will be block diagonal. Then think about its complement, if two vertices were in different connected component in the …

Oct 10, 2013 · Would you mind elaborating on what you mean by "two different components of G?" So far, I can assume that if u,v are vertices in G that are not connected by an edge, then …

This graph is the famous Petersen graph (common drawings of this graph are available online) and happens to arise often as a counterexample to many conjectures.

Jun 4, 2020 · What is a formal way to define a complement of a directed graph? On the wikipedia link -> Here it is not quite clear for me if we take the edges of the opposite direction.

Oct 31, 2013 · Let G be a simple graph with n vertices. What is the relation between the number of edges of G and the number of edges of the complement G'? In the example below, I noticed …

Mar 18, 2021 · So the complementary graph is certainly not always a complete bipartite graph, it could have more edges as well. But the important thing here is that this complete bipartite …

Jun 5, 2013 · Since there are 10 possible edges, there are at least $\binom {10} {5}/2=126$ possible pairs of graph-complement pairs. But after making drawings for the same problem …

Jun 19, 2015 · In your given graph, there are $6$ vertices so in the complete graph K6,degree of each vertex will be $ (n-1) = 6-1 =5$ So degree sequence of a complement of your given …

May 30, 2015 · What are the conditions for the complement of a connected graph to be connected? In particular, when is the complement of a connected regular graph connected? I …

If G be a graph with diameter (G) $\geq$ 3. Prove that the diameter (G′) $\leq$ 3. where G' is the complement graph. This answer is similar to @Luiz answer but little bit more explained as it …