娄贞贞,黄琼湘.一类六角系统图的特征多项式及应用[J].数学研究及应用,2014,34(3):265~277
一类六角系统图的特征多项式及应用
On the Characteristic Polynomial of a Hexagonal System and Its Application
投稿时间:2013-04-22  最后修改时间:2013-07-09
DOI:10.3770/j.issn:2095-2651.2014.03.002
中文关键词:  特征多项式    六角系统  循环矩阵  能量  
英文关键词:characteristic polynomial  spectrum  hexagonal system  circulant matrix  energy  nullity.
基金项目:国家自然科学基金 (Grant No.11261059).
作者单位
娄贞贞 新疆大学数学与系统科学学院, 新疆 乌鲁木齐 830046 
黄琼湘 新疆大学数学与系统科学学院, 新疆 乌鲁木齐 830046 
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中文摘要:
      $L_n$表示直链六角系统图, $F_n$表示环链六角系统图, $M_n$表示M\"{o}bius环链六角系统图. 1968年, Derflinger和Sofer用群论的方法给出了$L_n$和$F_n$的特征多项式. 之后, Gutman通过使用Godsil和McKay的一个多项式的结果给出了这两类图的谱. 本文采用一种直接的办法给出了$F_n$和$L_n$的特征多项式和谱,并用这个办法给出了$M_n$的特征多项式和谱,这是个新结果. 另外,我们还得到了这三类图的零度和能量,考虑了$L_n$和 $M_n$的界.
英文摘要:
      Let $L_n$ be the hexagonal chain graph,$F_n$ be the hexacyclic system graph and $M_n$ be the M\"{o}bius hexacyclic system graph. Derflinger and Sofer gave the of $L_n$ and $F_n$ by using group theoretical method. Later, Gutman gave the spectra of them using a polynomial result due to Godsil and McKay. In this paper, we givespectra a simple and direct method to determine the characteristic polynomial and spectra of $F_n$ and $L_n$. By the method, we give the characteristic polynomial and spectrum of $M_n$ that is new. Additionally, the exact values of total $\pi$-electron energy and the nullities of $L_n$, $F_n$ and $M_n$ are obtained, and the bounds for the energy of $L_n$ and $M_n$ are also considered.
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