On an extremal problem related to a theorem of Whitney

A well known theorem of Whitney states that for any graph G,κ(G)⩽κ′(G)⩽δ(G).κ(G)⩽κ′(G)⩽δ(G).For any set of positive integers a,b,ca,b,c, a⩽b⩽ca⩽b⩽c, we determine the least order and the least size among all graphs with κ=aκ=a, κ′=bκ′=b and δ=cδ=c. We also show that there exist graphs of all orders greater than or equal to the least order among those graphs with κ=aκ=a, κ′=bκ′=b and δ=cδ=c.