A graph and its complement with specified properties I: connectivity
Jin Akiyama, Frank Harary · International Journal of Mathematics and Mathematical Sciences · 1979
We investigate the conditions under which both a graph G and its complement possess a specified property. In particular, we characterize all graphs G for which G and both (a) have connectivity one, (b) have line‐connectivity one, (c) are 2‐connected, (d) are forests, (e) are bipartite, (f) are outerplanar and (g) are eulerian. The proofs are elementary but amusing.