Questions, conjectures, and data about multiplicity lists for trees

We review and discuss a number of questions and conjectures about multiplicity lists occurring among real symmetric matrices whose graph is a tree. Our investigation is aided by a new electronic database containing all multiplicity lists for trees on fewer than 12 vertices. Some questions and conjectures are familiar and some are new, and new information is given about several. (C) 2016 Elsevier Inc. All rights reserved