The Five-Bead Chain Theorem for Polyhedranes

林映廷, 金必耀, 珠串組合分子模型—多面體烷的五珠串定理, 化學 第七十七卷第四期 405-411 頁 2019.

Ying-Ting Lin and Bih-Yaw Jin, Bead Chain Molecular Models: Five-bead Chain Theorem, CHEMISTRY (Chemical Society Located in Taipei) Vol. 77, No. 4, pp. 405-411, 2019.
DOI: 10.6623/chem.201912_77(4).002

This research paper mathematically proves that any polyhedrane molecule (CnHn) can be constructed using only five-bead chains, where each chain represents specific chemical bonds. The proof utilizes Peterson's perfect matching theorem to demonstrate the existence of resonance structures in fullerene graphs. The authors connect the arrangement of beads in the model to the concept of perfect matchings in graph theory. This innovative molecular model provides a visual representation of molecular structures, including resonance structures. The paper also explores non-uniform chain lengths and Hamilton cycles within the molecular structures.

Podcast: The Five-Bead Chain Theorem for Polyhedranes