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

Abstract

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.

Keywords

• graph
• complement
• girth
• circumference.