This proceedings volume gathers selected, revised papers presented at the 51st Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2020), held at Florida Atlantic University in Boca Raton, USA, on March 9-13, 2020. The SEICCGTC is broadly considered to be a trendsetter for other conferences around the world – many of the ideas and themes first discussed at it have subsequently been explored at other conferences and symposia.The conference has been held annually since 1970, in Baton Rouge, Louisiana and Boca Raton, Florida. Over the years, it has grown to become the major annual conference in its fields, and plays a major role in disseminating results and in fostering collaborative work.