Combinatorics Graph Theory and Computing : SEICCGTC 2020 Boca Raton USA March 9–13 Ratio Balancing Numbers(Bartz et al) An Unexpected Digit Permutation from Multiplying in any Number Base(Qu et al) A & Z Sequences for Double Riordan Arrays (Branch et al) Constructing Clifford Algebras for Windmill and Dutch Windmill Graphs; A New Proof of The Friendship Theorem(Myers) Finding Exact Values of a Character Sum (Peart et al) On Minimum Index Stanton 4 cycle Designs (Bunge et al) k Plane Matroids and Whiteley’s Flattening Conjectures (Servatius et al) Bounding the edge cover of a hypergraph (Shahrokhi) A Generalization on Neighborhood Representatives (Holliday) Harmonious Labelings of Disconnected Graphs involving Cycles and Multiple Components Consisting of Starlike Trees(Abueida et al) On Rainbow Mean Colorings of Trees (Hallas et al) Examples of Edge Critical Graphs in Peg Solitaire (Beeler et al) Regular Tournaments with Minimum Split Domination Number and Cycle Extendability (Factor et al) Independence and Domination of Chess Pieces on Triangular Boards and on the Surface of a Tetrahedron(Munger et al) Efficient and Non efficient Domination of Z stacked Archimedean Lattices (Paskowitz et al) On subdivision graphs which are 2 steps Hamiltonian graphs and hereditary non 2 steps Hamiltonian graphs (Lee et al) On the Erd}os S_os Conjecture for graphs with circumference at most k + 1 (Heissan et al) Regular graph and some vertex deleted subgraph (Egawa et al) Connectivity and Extendability in Digraphs (Beasle) On the extraconnectivity of arrangement graphs (Cheng et al) k Paths of k Trees(Bickle) Rearrangement of the Simple Random Walk(Skyers et al) On the Energy of Transposition Graphs(DeDeo) A Smaller Upper Bound for the (4; 82) Lattice Site Percolation Threshold(Wierman). 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 field and plays a major role in disseminating results and in fostering collaborative work. This volume is intended for the community of pure and applied mathematicians in academia industry and government working in combinatorics and graph theory as well as related areas of computer science and the interactions among these fields.