Project Euler Forum

Can someone please explain to me what the definitions of a tree and a degree are? Because I don't understand why, for example, a line of 7 vertices, each connected to the next vertex with an edge, doesn't satisfy the conditions?

A tree is a connected graph with no loops. So a collection of vertices, with edges between them, such that for any pair of vertices there is exactly one path between them. The degree of a vertex is the number of edges attached to it.

All of the examples in the problem are trees. The top-left one has one vertex of degree 6 and six of degree 1. It's peerless because none of the vertices with degree 1 are directly connected with an edge.

Your example, A--B--C--D--E--F--G, is a tree, but there's an edge between vertices B and C, which are both degree 2. So it is not peerless.

(It's worth pointing out that the vertices are not labelled. A--B--C and A--C--B are the same tree with different labelling. I've only given your example labels to make it possible to talk about it)