Question

In Exercises \({\rm{3 - 5}}\)determine whether two given graphs are isomorphic.

Short answer

The given two graphs are isomorphic.

Step-by-step solution

Determine whether or not two graphs are isomorphic.

Although the isomorphism is difficult to locate, these graphs are isomorphic. Drawing the complement of each graph is one method that might lead to isomorphism. Because the complements contain fewer edges, they are easier to understand than the original graphs. It's simple to create a planar representation for each when you do this. May then identify an isomorphism by comparing the sizes of the areas. \({{\rm{u}}_{\rm{1}}} \Leftrightarrow ,{{\rm{v}}_{\rm{5}}},{u_2} \Leftrightarrow ,{{\rm{v}}_{\rm{4}}},{u_3} \Leftrightarrow ,{v_7},{u_4} \Leftrightarrow ,{v_3},{u_5} \Leftrightarrow ,{v_8},{u_6} \Leftrightarrow ,{v_2},{u_7} \Leftrightarrow ,{v_6},and{u_8} \Leftrightarrow ,{v_1}\)is one of these exchanges.

It's important to double-check that this correspondence keeps all of the edges.

Result.

Therefore, the given two graphs are isomorphic.