Wikipedia:Reference desk/Archives/Mathematics/2011 June 8

= June 8 =

Example of a graph
Can someone please give me an example of a k-regular connected graph G, (k>2) which has order 4 or more and contains a triangle but no square?-Shahab (talk) 06:14, 8 June 2011 (UTC)


 * I have an example of order 10, but I'm going to have to draw it. I did a quick search on Commons to see if there was already an image of it there, and I found the Markström graph (see right), which is another example. —Bkell (talk) 07:20, 8 June 2011 (UTC)


 * The Dürer graph is also an example. —Bkell (talk) 07:22, 8 June 2011 (UTC)


 * And Tietze's graph. (I'm running through the list at Graphs in graph theory, by the way.) —Bkell (talk) 07:25, 8 June 2011 (UTC)


 * Three of the truncated Platonic solids, too. The truncated tetrahedron is pretty close to the example I came up with; here's a poor attempt to draw my example (the O's are the vertices):

O-O / \      / \  /   \     /   \ O-O   O-O \    \ /     /   \     O     / \   |    /     \   O   / \ / \ /      O---O —Bkell (talk) 07:40, 8 June 2011 (UTC)