Graph theory
question - is K1,3 the same as K4
my answer - i think yes because the numbers symbolise the number of vertices.
can someone confirm and explain in detail .
In graph theory, K1,3 and K4 are not the same graphs. Let me explain why.
The notation K1,3 represents a complete bipartite graph where one set of vertices has 1 vertex and the other set of vertices has 3 vertices. In other words, K1,3 has a subset of 1 vertex connected to a subset of 3 vertices, and there are no other edges between any of the vertices within the subsets. This can be visualized as a single vertex connected to three other vertices like the branches of a tree.
On the other hand, K4 represents a complete graph with 4 vertices. In a complete graph, each vertex is connected to every other vertex, forming a total of (n-1) edges for n vertices. In the case of K4, there will be a total of 6 edges connecting the 4 vertices.
So, K1,3 and K4 have different structures and different numbers of edges. K1,3 is a bipartite graph with 4 edges, while K4 is a complete graph with 6 edges. Therefore, they are not the same graph.