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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.
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 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.
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 ...
Instead, BRI quantifies body girth as well as height, potentially providing more accurate estimates of fat mass. BRI scores range from 1 to 16, with most people between 1 and 10, although people with scores of 6.9 and up – indicating wider, rounder bodies – were found to have a risk of all-cause mortality that was increased by up to 49% ...
The Tutte (3,8)-cage.. In the mathematical field of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.. Formally, an (r, g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has a length of exactly g.
girth The girth of a graph is the length of its shortest cycle. graph The fundamental object of study in graph theory, a system of vertices connected in pairs by edges. Often subdivided into directed graphs or undirected graphs according to whether the edges have an orientation or not. Mixed graphs include both types of edges. greedy