- Vertices
- n
- Edges
- n ( n − 1 ) 2 {\displaystyle \textstyle {\frac {n(n-1)}{2}}}
- Radius
- { 0 n ≤ 1 1 otherwise {\displaystyle \left\{{\begin{array}{ll}0&n\leq 1\\1&{\text{otherwise}}\end{array}}\right.}
- Diameter
- { 0 n ≤ 1 1 otherwise {\displaystyle \left\{{\begin{array}{ll}0&n\leq 1\\1&{\text{otherwise}}\end{array}}\right.}
- Girth
- { ∞ n ≤ 2 3 otherwise {\displaystyle \left\{{\begin{array}{ll}\infty &n\leq 2\\3&{\text{otherwise}}\end{array}}\right.}
- Automorphisms
- n ! ( S n )
- Chromatic number
- n
- Chromatic index
- n if n is odd n − 1 if n is even
- Spectrum
- { ∅ n = 0 { 0 1 } n = 1 { ( n − 1 ) 1 , − 1 n − 1 } otherwise {\displaystyle \left\{{\begin{array}{lll}\emptyset &n=0\\\left\{0^{1}\right\}&n=1\\\left\{(n-1)^{1},-1^{n-1}\right\}&{\text{otherwise}}\end{array}}\right.}
- Properties
- ( n − 1) -regular Symmetric graph Vertex-transitive Edge-transitive Strongly regular Integral