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The girth of an undirected graph can be computed by running a breadth-first search from each node, with complexity () where is the number of vertices of the graph and is the number of edges. [7] A practical optimization is to limit the depth of the BFS to a depth that depends on the length of the smallest cycle discovered so far. [ 8 ]
In three-dimensional geometry, the girth of a geometric object, in a certain direction, is the perimeter of its parallel projection in that direction. [ 1 ] [ 2 ] For instance, the girth of a unit cube in a direction parallel to one of the three coordinate axes is four: it projects to a unit square , which has four as its perimeter.
In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is the girth of its dual matroid . Matroid girth generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, Hall sets in bipartite graphs , even sets in families of ...
Some examples are the even cycles C 2n, the complete bipartite graphs K n,n with girth four, the Heawood graph with degree 3 and girth 6, and the Tutte–Coxeter graph with degree 3 and girth 8. More generally it is known that, other than the graphs listed above, all Moore graphs must have girth 5, 6, 8, or 12. [ 6 ]
Any objection to this equation rests primarily with the subjective nature of F 1 and F 2. The value 75.4 = 24 π , where 24 π substitutes for factor of 12 π in the formula for a volume of frustum of a cone encompassing a full tree using one base circumference, converting it to a volume formula that uses a basal circumference that is the ...
The math template formats mathematical formulas generated using HTML or wiki markup. (It does not accept the AMS-LaTeX markup that <math> does.) The template uses the texhtml class by default for inline text style formulas, which aims to match the size of the serif font with the surrounding sans-serif font (see below).
In functional analysis, the girth of a Banach space is the infimum of lengths of centrally symmetric simple closed curves in the unit sphere of the space. Equivalently, it is twice the infimum of distances between opposite points of the sphere, as measured within the sphere.
Girth is a measurement of the distance around the trunk of a tree measured perpendicular to the axis of the trunk. [18] Use of girth to arrive at an equivalent diameter is an older forestry measurement that is still used. In the United States girth is measured at a height of 4.5 feet above ground level.