In graph theory, a discipline within mathematics, a strongly regular graph is defined as follows. Let G = (V,E) be a regular graph with v vertices and degree k. G is said to be strongly regular if there are also integers λ and μ such that:
- Every two adjacent vertices have λ common neighbours.
- Every two non-adjacent vertices have μ common neighbours.
A graph of this kind is sometimes said to be an srg(v,k,λ,μ).
Some authors exclude graphs which satisfy the definition trivially, namely those graphs which are the disjoint union of one or more equal-sized complete graphs, and their complements, the Turán graphs.
A strongly regular graph is a distance-regular graph with diameter 2, but only if μ is non-zero.
Read more about Strongly Regular Graph: Properties, Examples, See Also
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Famous quotes containing the words graph, strongly and/or regular:
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
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“The fact is popular art dates. It grows quaint. How many people feel strongly about Gilbert and Sullivan today compared to those who felt strongly in 1890?”
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“What was that?” inquired Alice.
“Reeling and Writhing, of course, to begin with,” the Mock Turtle replied; “and then the different branches of Arithmetic—Ambition, Distraction, Uglification, and Derision.”
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