Multiplicity lists by diameter: All trees of diameter <7

This paper considers the problem of determining all multiplicity lists occurring among Hermitian matrices whose graph is a given tree from a new perspective. For all trees of diameter <7, it is shown how to generate all possible lists. For diameter 5 and 6, this includes many nonlinear trees. In the process, for diameter 4 (double stars), the first succinct and direct description of all ordered lists, for each instance, is given. Observations of topological relationships are helpful.