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For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.
The Heawood graph (top) is the smallest trivalent graph with girth 6; the Petersen graph (middle) is the smallest trivalent graph with girth 5; The Tutte eight cage (bottom) is the smallest trivalent graph with girth 8:
In common usage, girth refers to the circumference of a cylindrical object such as a tree trunk