International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 4, Pages 685-692

A graph and its complement with specified properties III: girth and circumference

Jin Akiyama and Frank Harary

Department of Mathematics, The University of Michigan, Ann Arbor 48109, Michigan, USA

Received 5 April 1979

Copyright © 1979 Jin Akiyama and Frank Harary. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.