Describe the automorphism group of the graph P4SolutionAn is

Describe the automorphism group of the graph P4

Solution

An isomorphism from a graph G to G is called an Automorphism of G.

G is said to be vertex transitive if for every pair u,vV(G) there is an automorphism that maps u to v.

Suppose G is a P4 with vertex set {1,2,3,4} and edge set {12,23,34}. There are two automorphisms for this graph as 1, 2; such that 1:V(G)V(G) defined by 1(v)= 2(4)=1. Also, the function 3: V(G)V(G) defined by 3(1)=2, 2(2)=1, 2(3)=3, 2(4)=1 is no way an automorphism of G, though G is isomorphic to the graph with vertex set {1, 2, 3, 4} and edge set {21, 13, 34}