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.”

—Marshall McLuhan (1911–1980)

“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?”

—Stephen Sondheim (b. 1930)

““I couldn’t 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 Arithmetic—Ambition, Distraction, Uglification, and Derision.”

“I never heard of ‘Uglification,’” Alice ventured to say.”

—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)