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.
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Famous quotes containing the words graph, strongly and/or regular:
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“I couldnt afford to learn it, said the Mock Turtle with a sigh. I only took the regular course.
What was that? inquired Alice.
Reeling and Writhing, of course, to begin with, the Mock Turtle replied; and then the different branches of ArithmeticAmbition, Distraction, Uglification, and Derision.
I never heard of Uglification, Alice ventured to say.”
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