Girth

Girth generally refers to the circumference of a cylindrical object, such as a tree trunk.

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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.

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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.

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The Petersen graph is the smallest trivalent graph with girth 5. The Heawood graph is the smallest trivalent graph with girth 6. The Tutte eight cage is the smallest trivalent graph with girth 8.

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Image:Petersen graph.svg|The Petersen graph, of girth 5

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Image:Heawood graph.png|The Heawood graph, of girth 6

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Image:Tutte eight cage.png|The Tutte eight cage, of girth 8

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Graph theory: In mathematics and computer science, graph theory studies the properties of graphs. Informally, a graph is a set of objects called vertices (or nodes) connected by links called edges (or arcs) which can be directed (assigned a direction). Typically, a graph is designed as a set of dots (the vertices...

Cycle: A cycle (Latin "cyclus," from Greek "kuklos" meaning circle) is anything round, in the physical sense (e.g. a bicycle) or in a temporal sense (e.g. the cycle of the seasons). Cyclic or cyclical are the adjective forms. Pages about cycles include:...

Infinity: :For the automobile brand, see Infiniti. For the radio company, see Infinity Broadcasting....

Girth related Images and Photos (experimental)

Ralphie May: Girth of a Nation

Ralphie May: Girth of a Nation