I want to draw a graph on the genus 1 surface. The graph has
2 vertex, 6 edges and 4 faces hence it by Euler Characteristics formula it lives on genus 1 surface.
I want to add an extra condition that I want 3 faces of degree 2 and 1 face of degree 6. Apriori I don't know if such a graph would exist? It also satisfies handshaking lemma.
I could imagine a graph in a sphere and draw it having
2 vertex, 6 edges and 6 faces. Any vizulaztion help or a picture would really help me in this case.
Best Answer
Here’s a start. Draw the torus as a square with sides identified, and draw the following graph:
This graph has two vertices (red and blue), four edges, and two faces (green and yellow). Can you modify this graph to add two extra edges and two extra faces?
With the change in requirements, here is another approach:
This had two vertices, six edges, and four faces. Three faces have degree 2, and one has degree 6.