Tricyclic graphs with exactly two main eigenvalues
Xiaoxia Fan; Yanfeng Luo; Xing Gao
Open Mathematics (2013)
- Volume: 11, Issue: 10, page 1800-1816
- ISSN: 2391-5455
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topXiaoxia Fan, Yanfeng Luo, and Xing Gao. "Tricyclic graphs with exactly two main eigenvalues." Open Mathematics 11.10 (2013): 1800-1816. <http://eudml.org/doc/269005>.
@article{XiaoxiaFan2013,
abstract = {An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let G 0 be the graph obtained from G by deleting all pendant vertices and δ(G) the minimum degree of vertices of G. In this paper, all connected tricyclic graphs G with δ(G 0) ≥ 2 and exactly two main eigenvalues are determined.},
author = {Xiaoxia Fan, Yanfeng Luo, Xing Gao},
journal = {Open Mathematics},
keywords = {Main eigenvalues; Tricyclic graphs; 2-walk (a; b)-linear graphs; main eigenvalues; tricyclic graphs; 2-walk ()-linear graphs},
language = {eng},
number = {10},
pages = {1800-1816},
title = {Tricyclic graphs with exactly two main eigenvalues},
url = {http://eudml.org/doc/269005},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Xiaoxia Fan
AU - Yanfeng Luo
AU - Xing Gao
TI - Tricyclic graphs with exactly two main eigenvalues
JO - Open Mathematics
PY - 2013
VL - 11
IS - 10
SP - 1800
EP - 1816
AB - An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. Let G 0 be the graph obtained from G by deleting all pendant vertices and δ(G) the minimum degree of vertices of G. In this paper, all connected tricyclic graphs G with δ(G 0) ≥ 2 and exactly two main eigenvalues are determined.
LA - eng
KW - Main eigenvalues; Tricyclic graphs; 2-walk (a; b)-linear graphs; main eigenvalues; tricyclic graphs; 2-walk ()-linear graphs
UR - http://eudml.org/doc/269005
ER -
References
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- [7] Hu Z., Li S., Zhu C., Bicyclic graphs with exactly two main eigenvalues, Linear Algebra Appl., 2009, 431(10), 1848–1857 http://dx.doi.org/10.1016/j.laa.2009.06.022[WoS] Zbl1175.05085
- [8] Shi L., On graphs with given main eigenvalues, Appl. Math. Lett., 2009, 22(12), 1870–1874 http://dx.doi.org/10.1016/j.aml.2009.06.027[Crossref]
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