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Connected components of arithmetic graphs (1980)

Nathanson, Melvyn B.

Springer

Monatshefte für Mathematik 89 (1980), S. 219-222

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ISSN: 1436-5081

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Let $$R \subseteq \left\{ {1,2,...,m} \right\}$$ . LetG m (R) be the graph whose vertices are the numbers 1, 2, ...,m and whose edges are all pairs {a, b} such thata+b≡r (modm) for somer∈R. LetC m (R) be the number of connected components ofG m (R). Letd be the greatest common divisor ofm and the differencesr j −r j or allr i ,r j ∈R. ThenC m (R) is equal to (i) (d+1)/2 ifd is odd, (ii)d/2 ifd is even andr is odd for allr∈R, or (iii) (d/2)+1 ifd is even andr is even for allr∈R.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01295437

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