Complete bipartite graph:K1,3

This article defines a particular undirected graph, i.e., the definition here determines the graph uniquely up to graph isomorphism.
View a complete list of particular undirected graphs

Definition

This graph is defined as the complete bipartite graph $K_{1,3}$, i.e., it is a graph with 4 vertices and 3 edges, all sharing a common vertex, with the other vertex free to vary.

Explicit descriptions

Descriptions of vertex set and edge set

Vertex set: $\{1,2,3,4\}$

Edge set: $\{\{1,2\},\{1,3\},\{1,4\}\}$

Adjacency matrix

With the above ordering of vertices, the adjacency matrix is:

$\left(\begin{array}{cccc}0& 1& 1& 1\\ 1& 0& 0& 0\\ 1& 0& 0& 0\\ 1& 0& 0& 0\\ \end{array}\right)$

Arithmetic functions

Size measures

Function	Value	Explanation
size of vertex set	4	As $K_{m,n},m=1,n=3$: $m+n=1+3=4$
size of edge set	3	As $K_{m,n},m=1,n=3$: $mn=(1)(3)=3$