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A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan
A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan
CSE Technical Reports
We derive the numerical value of the fine structure constant in purely number-theoretic terms, under the assumption that in a system of charges between two parallel conducting plates, the Casimir energy and the mutual Coulomb interaction energy agree.
Isomorph-Free Generation Of 2-Connected Graphs With Applications, Derrick Stolee
Isomorph-Free Generation Of 2-Connected Graphs With Applications, Derrick Stolee
CSE Technical Reports
Many interesting graph families contain only 2-connected graphs, which have ear decompositions. We develop a technique to generate families of unlabeled 2-connected graphs using ear augmentations and apply this technique to two problems. In the first application, we search for uniquely Kr-saturated graphs and find the list of uniquely K4-saturated graphs on at most 12 vertices, supporting current conjectures for this problem. In the second application, we verify the Edge Reconstruction Conjecture for all 2-connected graphs on at most 12 vertices. This technique can be easily extended to more problems concerning 2-connected graphs.