|
In graph theory, 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). Strongly regular graphs were introduced by Raj Chandra Bose in.〔https://projecteuclid.org/euclid.pjm/1103035734, R. C. Bose, Strongly regular graphs, partial geometries and partially balanced designs, Pacific J. Math 13 (1963) 389–419. (p. 122)〕 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,〔(Brouwer, Andries E; Haemers, Willem H. ''Spectra of Graphs''. p. 101 )〕〔Godsil, Chris; Royle, Gordon. ''Algebraic Graph Theory''. Springer-Verlag New York, 2001, p. 218.〕 and their complements, the Turán graphs. The complement of an srg(''v'', ''k'', λ, μ) is also strongly regular. It is an srg(''v'', ''v−k''−1, ''v''−2−2''k''+μ, ''v''−2''k''+λ). A strongly regular graph is a distance-regular graph with diameter 2, but only if μ is non-zero. ==Properties== 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Strongly regular graph」の詳細全文を読む スポンサード リンク
|