0
credit always involves parties: the debtor who obtains the money, goods or services in exchange of his promise to pay at a future date
Still curious? Ask our experts.
Chat with our AI personalities
Vivi
Beau
TaigaAdd your answer:
Earn +20 pts
What is the automorphism group of a complete bipartite graph?
The automorphism group of a complete bipartite graph K_n,n is (S_n x S_n) semidirect Z_2.
How do you count spanning trees in a graph?
Cayleys formula states that for a complete graph on nvertices, the number of spanning trees is n^(n-2). For a complete bipartite graph we can use the formula p^q-1 q^p-1. for the number of spanning trees. A generalization of this for any graph is Kirchhoff's theorem or Kirchhoff's matrix tree theorem. This theorem looks at the Laplacian matrix of a graph. ( you may need to look up what that is with some examples). For graphs with a small number of edges and vertices, you can find all the spanning trees and this is often quicker. There are also algorithms such as depth-first and breadth-first for finding spanning trees.
What is a divisor graph?
Let S be a finite, non-empty set of positive integers. The divisor graph G(S) of S has S as its vertex set, and two distinct vertices i and j are adjacent if and only if either idivides j or j divides i. Let G be a simple graph. Then G is called a divisor graph if G is isomorphic to G(S) for some non-empty, finite set S of positive integers.REFERENCE :S. Ganesan, D. Uthayakumar, Corona of Bipartite Graphs with Divisor GRaphs Produce New Divosor Graphs,Bulletin of Kerala Mathematics AssociationVol.9, No.1, (2012, June) 219-226
