On the Characteristic Polynomial of a Hexagonal System and Its Application
Received:April 22, 2013  Revised:July 09, 2013
Key Words: characteristic polynomial   spectrum   hexagonal system   circulant matrix   energy   nullity.  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11261059).
Author NameAffiliation
Zhenzhen LOU College of Mathematics and Systems Science, Xinjiang University, Xinjiang 830046, P. R. China 
Qiongxiang HUANG College of Mathematics and Systems Science, Xinjiang University, Xinjiang 830046, P. R. China 
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Abstract:
      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.
Citation:
DOI:10.3770/j.issn:2095-2651.2014.03.002
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