Spectrum of complete bipartite graph - Mathematics Stack Exchange
2021年4月27日 · Prove that a complete bipartite graph with n + m nodes has a spectrum $(\sqrt{mn} ,0,..,0,-\sqrt{mn})$ Prove that a complete graph with n nodes has a spectrum $(n …
Genus of a complete bipartite graph - Mathematics Stack Exchange
2020年1月5日 · In Harary, F. Graph Theory, the result is only stated (and the easy lower bound explained). 2. Nice alternative proof in A. Bouchet, Orientable and nonorientable genus of the …
Example for adjacency matrix of a bipartite graph
When a (simple) graph is "bipartite" it means that the edges always have an endpoint in each one of the two "parts". So if the vertices are taken in order, first from one part and then from …
Maximum number of edges in a bipartite graph
2015年1月10日 · Prove that for a bipartite graph $G$ on $n$ vertices the number of edges in $G$ is at most $\\frac{n^2}{4}$. I used induction on $n$. Induction hypothesis: Suppose ...
Perfect matching in a graph and complete matching in bipartite …
When I google for complete matching, first link points to perfect matching on wolfram. It defines perfect matching as follows: A perfect matching of a graph is a matching (i.e., an independent ...
Diameter of bipartite graph - Mathematics Stack Exchange
2019年7月19日 · I know that a complete bipartite graph k_{n,m} has a diameter equals one when m=n=1 and 2 otherwise. My question is about a bipartite graph K_{n,n} with two partite sets of …
Complement of a bipartite graph - Mathematics Stack Exchange
2015年1月29日 · What constraint must be placed on a bipartite graph G to guarantee that G's complement will also be bipartite? I see someone saying that it can't be 4 or more in each …
What is the automorphism group of a complete bipartite graph?
2022年7月3日 · Determine the automorphism group of the complete bipartite Graph $\mathcal{V}_{m,n}$. Some definitions: A complete bipartite graph is a special kind of bipartite …
Complement of the complete bipartite graph - Mathematics Stack …
the complement of bipartite graph is perfect Hot Network Questions Emma Peel (Diana Rigg) quotation from "The Avengers" (original TV show, not Marvel)
Eigenvalues of a bipartite graph - Mathematics Stack Exchange
2012年10月27日 · In an undirected graph, the only possible period is $2$. Thus the graph decomposes into the sets of vertices that are even and odd with respect to that period, and is …