A graph and its complement with specified properties III: girth and circumference - Jin Akiyama; Frank Harary (International Journal of Mathematics and Mathematical Sciences)
In this series, we investigate the conditions under which both a graph G and its complement G¯ possess certain specified properties. We now characterize all the graphs G such that both G and G¯ have the same girth. We also determine all G such that both G and G¯ have circumference 3 or 4.