Complete bipartite graph:K3,3: Difference between revisions

Revision as of 20:16, 29 May 2012

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 undirected graph is defined as the complete bipartite graph $K_{3,3}$ . Explicitly, it is a graph on six vertices divided into two subsets of size three each, with edges joining every vertex in one subset to every vertex in the other subset.

Explicit descriptions

Descriptions of vertex set and edge set

We provide a description where the vertex set is $\{1,2,3,4,5,6\}$ and the two parts are $\{1,2,3\}$ and $\{4,5,6\}$ :

Vertex set: $\{1,2,3,4,5,6\}$

Edge set: $\{\{1,4\},\{1,5\},\{1,6\},\{2,4\},\{2,5\},\{2,6\},\{3,4\},\{3,5\},\{3,6\}\}$

Adjacency matrix

The adjacency matrix is as follows:

${\begin{pmatrix}0&0&0&1&1&1\\0&0&0&1&1&1\\0&0&0&1&1&1\\1&1&1&0&0&0\\1&1&1&0&0&0\\1&1&1&0&0&0\\\end{pmatrix}}$

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 This [[undirected graph]] is defined as the [[complete bipartite graph]] <math>K_{3,3}</math>. Explicitly, it is a graph on six vertices divided into two subsets of size three each, with edges joining every vertex in one subset to every vertex in the other subset.
+==Explicit descriptions==
+===Descriptions of vertex set and edge set===
+We provide a description where the vertex set is <math>\{ 1,2,3,4,5,6\}</math> and the two parts are <math>\{ 1,2,3\}</math> and <math>\{ 4,5,6 \}</math>:
+Vertex set: <math>\{ 1,2,3,4,5,6 \}</math>
+Edge set: <math>\{ \{ 1,4 \}, \{ 1,5 \}, \{ 1,6 \}, \{ 2,4 \}, \{ 2,5 \}, \{ 2,6 \}, \{ 3,4 \}, \{ 3,5 \}, \{ 3, 6 \} \}</math>
+===Adjacency matrix===
+The adjacency matrix is as follows:
+<math>\begin{pmatrix} 0 & 0 & 0 & 1 & 1 & 1 \\0 & 0 & 0 & 1 & 1 & 1 \\0 & 0 & 0 & 1 & 1 & 1 \\ 1 & 1 &1 & 0 & 0 & 0 \\1 & 1 &1 & 0 & 0 & 0 \\1 & 1 &1 & 0 & 0 & 0 \\\end{pmatrix}</math>