Girth is the circumference of a cylindrical object. The circumference is the distance around a closed curve. ...

Girth is sometimes used by postal services and delivery companies as basis for pricing. For example (for at least one delivery company), if you have a box to ship, it has three sides: length (the longest side) and height and width. The girth in this case is 2 * (height + width).

In graph theory, the girth of a graph pen is the length of the shortest cycle contained in the graph. If the graph does not 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 is 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 called triangle-free. A pictorial representation of a graph In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. ... In graph theory, a path in a graph is a sequence of vertices such that from each of its vertices there is an edge to the next vertex in the sequence. ... This article or section is not written in the formal tone expected of an encyclopedia article. ... In the mathematical field of graph theory, a cubic graph is a graph where all vertices have degree 3. ... The Tutte (3,8)-cage. ... The Petersen graph Another drawing of the Petersen graph, with only two crossings Another drawing, with each edge the same length The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory. ... The Heawood graph, of girth 6 In the mathematical field of graph theory, a Heawood graph is the 6-cage, the smallest cubic graph of girth 6. ... In the mathematical field of graph theory, the Tutte eight cage is the smallest cubic graph of girth 8. ... In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges. ...

The Petersen graph, of girth 5 Image File history File links This is a lossless scalable vector image. ... The Petersen graph Another drawing of the Petersen graph, with only two crossings Another drawing, with each edge the same length The Petersen graph is a small graph that serves as a useful example and counterexample in graph theory. ...

The Heawood graph, of girth 6 Image File history File links Heawood_graph. ... The Heawood graph, of girth 6 In the mathematical field of graph theory, a Heawood graph is the 6-cage, the smallest cubic graph of girth 6. ...

The Tutte eight cage, of girth 8 Image File history File links Tutte_eight_cage. ... In the mathematical field of graph theory, the Tutte eight cage is the smallest cubic graph of girth 8. ...

See also

• Systolic geometry