My project focused on the study of amino acids using mathematical and chemical graph theory. Here's the abstract for my paper: Amino acids are the building blocks of proteins. There are twenty different amino acids and five different amino acid groups. Each amino acid contains a carboxyl group, an amino group, a central carbon and hydrogen, and a side chain or R group, with the exception of Proline which has an imino group, instead of an amino group. Graph theory is a branch of mathematics used to study graphs, which are a collection of points called vertices and a set of connecting lines, called edges. Amino acids have been displayed as tree graphs. Tree graphs are connected graphs containing no cycles. Amino acids can be classified and grouped using graphical invariants. Graphical invariants such as diameter, weighted domination number, average weight of an edge, weighted sum of peripheral vertices, and the minimum weight of all paths of a certain length were used to study the amino acids in the past. Spanning sub-graphs were then used to construct sub-graphs which grouped amino acids into very informative trees. The current research is graphing amino acids by using multi-graphs, which are graphs that may contain multi-edges and cycles. After representing the amino acids as multi-graphs, we can then use a mixture of mathematical graph theory and chemical graph theory invariants such as domination number, total domination number, independent domination number, global alliance, total weight, peripheral vertices weight, Zagreb group indices, Hoyosa z-index, and connectivity order indices to study the amino acids. Dendrograms, which are diagrams used to branch different hierarchy categories based on similarity of different variables using their invariants, were then constructed to help categorize and study amino acids.
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