All Questions

The Cayley graph of $A_5$ with two generators of order 5 seems rather complicated. What is its graph genus (orientable or non-orientable)? The best I could get by trial and error is an embedding ...

Given a graph the minimum genus $g$ is the minimum number of handles needed so that there an imbedding of the graph on the surface with no edge crossings. If the graph is of genus $g$ then is there ...

The first picture below has $v=12$ vertices, $e=16$ edges, and seems to have $k=4$ crosscaps (denoted by something like $\oplus$). The number of faces $f$ should satisfy $$v-e+f=2-k$$ which gives $f=2$...

Suppose we have a graph G. Is it true that we can map its vertices to the plane such that when connecting neighboring vertices with segments, then any induced cycle of G that has length at least 4 ...

A generic question: are there any spectral techniques to estimate the genus of a graph? I am interested in complete balance multipartite graph.