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Moore-s Method is a form of inquiry-based learning. R.L. Moore is a legendary figure behind this method, who started this method in an extreme way at the Mathematics Department, University of Texas in 1920-s. Despite the controversies it instilled, the method, or some milder versions of the method remain popular as a constructivist way to learn deep mathematics through inquiry-based learning. We report an implementation of Moore-s Method to a small group of students in learning new topics for their theses in two semester terms. The topic of the discussions was Spectral Properties of Quantum Graphs. By the nature of the method we tried to limit the use of textbooks or research articles for reference; almost everything that was needed for construction was produced independently within the discussions. Due to various background level they had already possessed in the beginning, the group started rather slowly. As they started to grasp better on the subject, the discussion pick up some pace, and the role of instructor started to diminish, to a mere facilitator. At the end of the second semester the group had gained significant confidence, proved a few results in some uncharted or less charted territory of Quantum Graph. The trial implementation of Moore-s method was deemed a success, as we gain some insight into the mechanics of the method: applicability and limitation, group size, topics covered, group interaction, assessment and indicators of success. References: 1. P. Blessinger, J.M. Carfora (eds.), Inquiry-Based Learning for Science Technology, Engineering and Math (STEM) Programs: A Conceptual and Practical Resource for Educators, Emerald 2015 2. C.A. Coppin et al, The Moore Method: A Pathway to Learner-Centered Instruction, MAA 2009 3. S.G. Krantz, How to Teach Mathematics, 2nd ed., AMS 1999