Vipul: Created page with "==Definition== Suppose $d$ and $g$ are positive integers, with $g \ge 3$ . Consider the collection of all finite undirected graphs that ar..."

2012-05-29T04:09:13Z

Created page with "==Definition== Suppose <math>d</math> and <math>g</math> are positive integers, with <math>g \ge 3</math>. Consider the collection of all finite undirected graphs that ar..."

New page

==Definition==

Suppose <math>d</math> and <math>g</math> are positive integers, with <math>g \ge 3</math>. Consider the collection of all finite [[undirected graph]]s that are <math>d</math>-[[regular graph]]s and have [[girth]] <math>g</math>. A <math>(d,g)</math>-cage is a graph in this collection that has the minimum possible number of vertices, i.e., there is no graph in the collection with fewer vertices.

If <math>d</math> is not explicitly specified, then we are referring to the case <math>d = 3</math>, i.e., to [[cubic graph]]s.

Cage - Revision history

Vipul: Created page with "==Definition== Suppose d and g are positive integers, with g \ge 3. Consider the collection of all finite undirected graphs that ar..."

Vipul: Created page with "==Definition== Suppose $d$ and $g$ are positive integers, with $g \ge 3$ . Consider the collection of all finite undirected graphs that ar..."