完全圖

Also known as complete digraph, complete graphs, complete digraphs, 2K1-free graph

任兩相異節點間洽有一條邊相連的無向圖

In the Vinony graph

Within Vinony's link graph, 完全圖 is referenced by 516 other articles, and connects out to graph, Császár polyhedron and mathematics.

It is catalogued under topics including Parametric families of graphs and Regular graphs.

Its subject is documented across 38 Wikipedia language editions.

Key facts

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
Notation: K n

via Wikipedia infobox

Wikidata facts

Subclass of: Moore graph
Image: Complete graph example.svg

Show 6 more facts

maintained by WikiProject: WikiProject Mathematics
Commons category: Complete graphs
graph diameter: 1
graph radius: 1
studied by: graph theory
opposite of: edgeless graph

Sources (2)

via Wikidata · CC0

Article · 中文

在图论中，完全图是一个简单的无向图，其中每一对不同的顶点都只有一条边相连。完全有向图是一个有向图，其中每一对不同的顶点都只有一对边相连（每个方向各一个）。图论起源于欧拉在1736年解决七桥问题上做的工作，但是通过将顶点放在正多边形上来绘制完全图的尝试，早在13世纪拉蒙·柳利的工作中就出现了。这种画法有时被称作神秘玫瑰。

Abstract from DBpedia / Wikipedia · CC BY-SA