A connected component of a graph is a maximal subset of nodes in the graph having the property for any two nodes in the subset, there exists a path of edges that connects them together. InFigure 10.3, it is easy to see the graph has twoconnected components {a, b, c} and {d, e}...
In this paper, we show that if G is a transitive permutation group of degree n having no non-trivial normal 2-subgroups such that the stabilizer of a point is a 2-group, then the minimal degree of G is at least 23n. The proof depends on the classification of finite simple groups...
Take any two elements,aandb. If , then (according to property (2)), which means (according to property (3)). It's very simple, isn't it? However, you noticed that Johnny's "proof" is wrong, and decided to show him a lot of examples that prove him wrong. Here's your task: c...