I had noticed that too. It was intended to be 2n-3, not 2n-4: 2n adjacent to 2n+1, 2n+2, 2n-2 2n+1 adjacent to 2n, 2n+5, 2n-3 The odd adjacencies can equivalently be expressed as: 2n+1 adjacent to (2n+1)-1, (2n+1)+4, (2n+1)-4 Each even number is adjacent to 1 odd and 2 even (the next higher odd, and the evens that are 2 away), and each odd number is adjacent to 1 even and 2 odd (the next lower even, and the odds that are 4 away). Tom Keith F. Lynch writes:

Allan Wechsler <acwacw@gmail.com> wrote:

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"Keith F. Lynch" <kfl@KeithLynch.net> wrote:

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Find a connected graph of girth 5 (i.e. no loops of size 3 or 4) in which every integer is a vertex, every vertex has the same valence, and every vertex is part of a loop of size 5.

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Yes, I have a solution, unless I'm confused.

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All even numbers 2n are connected to 2n+1, 2n+2, and 2n-2. All odd numbers 2n+1 are connected to 2n, 2n+5, and 2n-4. I am pretty sure this graph is cubic of girth 5.

3 is connected to 7, but 7 is not connected to 3.