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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.
What is the name of graphs?
line graph scatter graph
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 types of bar graphs are there?
pie graph, bar graph, and line graph.
How can you understand a given graph is Euler or not?
The definition of an Eulerian path is a path in a graph which visits each edge exactly once. Intuitively, think of tracing the path with a pencil without lifting the pencil's edge from the page. One definition of an Eulerian graph is that every vertex has an even degree. You can check this by counting the degrees. Please see the related link for details.
