  We classify all connected, simple, 3-regular graphs with girth at least 5
that are Ricci-flat. We use the definition of Ricci curvature on graphs given
in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct.
Anal., 2009. A graph is Ricci-flat, if it has vanishing Ricci curvature on all
edges. We show, that the only Ricci-flat cubic graphs with girth at least 5 are
the Petersen graph, the Triplex and the dodecahedral graph. This will correct
the classification in Lin-Lu-Yau, Comm. Anal. Geom., 2014, that misses the
Triplex.
