Girth Totally Explained

Everything about The Girth totally explained

The girth of an object is a measurement around it. It is sometimes used by postal services and delivery companies as a basis for pricing. For example, Canada Post requires that an item's length plus girth not exceed a maximum allowed value. For a rectangular box, the girth is 2 * (height + width), for example the perimeter of a cross section perpendicular to its length.
In graph theory, the girth of a graph is the length of the shortest cycle contained in the graph. If the graph doesn't contain any cycles, its girth is defined to be infinity. For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3. A cubic graph of girth

g

that's as small as possible is known as a

g

-cage. The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, and the Tutte eight cage is the unique 8-cage. A graph with girth ≥ 4 is triangle-free. Image:Petersen graph blue.svg|The Petersen graph, of girth 5 Image:Heawood graph.svg|The Heawood graph, of girth 6 Image:Tutte eight cage.svg|The Tutte eight cage, of girth 8 Further Information

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