臺灣國際科展

Lunar Tide Contribution to Thermosphere Weather

科展類別
臺灣國際科展作品
屆次
2015年
科別
地球與行星科學
得獎情形
一等獎
學校名稱
Fairview High School
作者
Jesse Zhang
備註
青少年科學獎

摘要或動機

Internet search technology is a pervasively used utility that relies on techniques from the _eld of spectral graph theory. We present a novel spectral approach to investigate an existing problem: the critical group of the line graph has been characterized for regular nonbipartite graphs, but the general regular bipartite case remains open. Because of the ine_ectiveness of previous techniques in regular bipartite graphs, our approach provides a new perspective and aims to obtain the relationship between the spectra of the Laplacians of the graph G and its line graph bG. We obtain a theorem for the spectra of all regular bipartite graphs and demonstrate its e_ectiveness by completely characterizing the previously unknown critical group for a particular class of regular bipartite graphs, the incidence graphs of _nite projective planes with square order. This critical group is found to be Z2_(Z2q+2)q3􀀀1_(Zq2+q+1)q2+q􀀀1; where q is the order of the _nite projective plane.


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