5
$\begingroup$

There is exactly one cubic planar graph with six 3-faces and six 7-faces (and no other faces). Surely it must have a name. What is it called?

Here is a picture of the graph embedded on the plane with a point at infinity:

(source)

A slightly more general question: How can I find out what the names are of semi-famous graphs? A graph is semi-famous if it has an established name but is not easily found in a standard textbook on the subject.

I did try the House of Graphs by searching using their drawing tool, but found nothing.

$\endgroup$

2 Answers 2

10
$\begingroup$

There are a few on Wikipedia: http://en.wikipedia.org/wiki/Category:Individual_graphs, and there are more on MathWorld: http://mathworld.wolfram.com/topics/SimpleGraphs.html. There is a page on Wikipedia with pictures: http://en.wikipedia.org/wiki/Gallery_of_named_graphs

Unfortunately I don't have an answer to your question, but I would call it a "partially truncated cube", where the non-truncated vertices are opposite. Accordingly, you could say that it is constructed from the truncated cube by performing a $\Delta$-$Y$ contraction on two maximally distant triangles. I'm moving this comment to an answer in order to attach a picture of the truncated cube:

truncated cube

$\endgroup$
1
  • 4
    $\begingroup$ You beat me to "partially truncated cube" while I was off looking for a good wikipedia reference. $\endgroup$
    – Lee Mosher
    Mar 8, 2013 at 16:53
2
$\begingroup$

Sage has search facilities for graphs with specified properties, and "knows" a large number of "named" graphs. As you work within a system running Python, you can do much more much easier, compared to what you get just by searching online databases using a www interface. The manual of the corresponding part is here.

$\endgroup$
2
  • $\begingroup$ I'm familiar with the Sage graph library, but not familiar with a functionality that allows me to give it a graph and ask for its name. The only thing I can think about is trying all graph.NAME objects and testing isomorphism (and some are parameterized). $\endgroup$ Mar 9, 2013 at 14:10
  • $\begingroup$ This is a bit of a hack, but you can do something like this: sage: import inspect sage: g=inspect.getmembers(graphs, predicate=inspect.isfunction) will give you a correspondence between graph names and functions to create these named graphs (not all of entries of g would correspond to actual named graphs, so you'd need to be a bit careful) $\endgroup$ Mar 9, 2013 at 16:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.