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). |
|
Hits: 2762 |
Download times: 2470 |
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 |
View Full Text View/Add Comment |