Consider a graph G with vertices $\{a,b,c,d,e,f\}$& edges $\{ac,ad,ae,af,bc,bd,be,bf,ce,cf,de,df\}$

I$)$ Sketch and label G$,$ also known as the complete tripartite graph $K_{2,2,2}.$

Sort the vertices of $G$ to into three sets to demonstrate its tripartite nature.

Sketch and label a drawing of $G$ with as few edge crossings you can.

Sketch and label subgraphs of $G$ to illustrate the structures named.

If no such structure exists within $G,$ explain why.

a$)$ a Hamiltonian cycle or Hamiltonian path

b$)$ an Eulerian circuit or Eulerian trail

c$)C_5,$ the cycle on five vertices

d$)K_4,$ the complete graph on four vertices Work on paper please