The May Time Graph

The May Time Graph is a non-simple, connected graph that is symmetrical. It can be divided into eight identical parts and involves 17 vertices. The graph was named after the resemblance of a flower inside the construction, which related to the saying "April showers bring May flowers".

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Questions:

1) Is the graph planar? Show why or why not.

2) What is the chromatic number, or the minimum number of different colors that can be used to color vertices so that no adjacent vertices are the same color, of this graph?

3) Does this graph have a subgraph that is complete bipartite? If so, identify it.

Sarah Byun, Created with GeoGebra