Is a bipartite graph symmetrical?
A bipartite graph has two sets of vertices, for example A and B, with the possibility that when an edge is drawn, the connection should be able to connect between any vertex in A to any vertex in B. If the graph does not contain any odd cycle (the number of vertices in the graph is odd), then its spectrum is symmetrical.
How many edges can a bipartite graph have?
Any bipartite graph consisting of ‘n’ vertices can have at most (1/4) x n 2 edges. Maximum possible number of edges in a bipartite graph on ‘n’ vertices = (1/4) x n 2. Suppose the bipartition of the graph is (V 1, V 2) where |V 1 | = k and |V 2 | = n-k. The number of edges between V 1 and V 2 can be at most k (n-k) which is maximized at k = n/2.
Can a bipartite graph be presented as two biadjacency matrices?
One major property is that any bipartite graph can be presented as two biadjacency matrices (or otherwise projections). While in an original bipartite graph, vertices which belong to a set are not connected to each other, in its biadjacency form they are connected through nodes that belong to the other set (indirect connections).
How many vertices does a bipartite graph K R S have?
The complete bipartite graph K r,s (where r,s ? 1) has two kinds of vertices: V + = {a 1 ,..., a r } and V ? = {b 1 ,..., b s }; and all possible edges between the two kinds: E = {a i b j for all i,j}. Question: How many edges in K r,s ? Let G be a bipartite graph with 7 vertices. What is the maximum possible number of edges for G?
Symmetric Bipartite Graphs and Graphs with Loops