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| Butterfly graph | |
|---|---|
 | |
| Vertices | 5 |
| Edges | 6 |
| Radius | 1 |
| Diameter | 2 |
| Girth | 3 |
| Automorphisms | 8 (D4) |
| Chromatic number | 3 |
| Chromatic index | 4 |
| Properties | Planar Unit distance Eulerian Not graceful |
| Table of graphs and parameters | |
In the mathematical field of graph theory, the butterfly graph (also called the bowtie graph and the hourglass graph) is a planar, undirected graph with 5 vertices and 6 edges.[1][2] It can be constructed by joining 2 copies of the cycle graph C3 with a common vertex and is therefore isomorphic to the friendship graph F2.
The butterfly graph has diameter 2 and girth 3, radius 1, chromatic number 3, chromatic index 4 and is both Eulerian and a penny graph (this implies that it is unit distance and planar). It is also a 1-vertex-connected graph and a 2-edge-connected graph.
There are only three non-graceful simple graphs with five vertices. One of them is the butterfly graph. The two others are cycle graph C5 and the complete graph K5.[3]
- ^ Weisstein, Eric W. "Butterfly Graph". MathWorld.
- ^ ISGCI: Information System on Graph Classes and their Inclusions. "List of Small Graphs".
- ^ Weisstein, Eric W. "Graceful graph". MathWorld.