TY - JOUR

T1 - Some results on graphs with exactly two main eigenvalues

AU - Hou, Yaoping

AU - Tang, Zikai

AU - SHIU, Wai Chee

N1 - Funding Information:
The first author was supported by the National Natural Science Fund of China (No. 10771061 , 11171102 ). The last author was supported by: GRF, Research Grant Council of Hong Kong ; FRG, Hong Kong Baptist University . The authors would like to express their sincere gratitude to the referees for careful reading and valuable suggestions, which led to a number of improvements in this work.

PY - 2012/10

Y1 - 2012/10

N2 - An eigenvalue of a graph G is called main if there is an associated eigenvector not orthogonal to j, the vector with each entry equal to 1. In this work, an error in a prior paper [Y. Hou and F. Tian, Unicyclic graphs with exactly two main eigenvalues, Appl. Math. Letters, 19 (2006), 1143-1147] is pointed out and the properties of the graphs with exactly two main eigenvalues and with pendent vertices are discussed. As an application, we obtain, together with known results, all connected bicyclic and tricyclic graphs with exactly two main eigenvalues.

AB - An eigenvalue of a graph G is called main if there is an associated eigenvector not orthogonal to j, the vector with each entry equal to 1. In this work, an error in a prior paper [Y. Hou and F. Tian, Unicyclic graphs with exactly two main eigenvalues, Appl. Math. Letters, 19 (2006), 1143-1147] is pointed out and the properties of the graphs with exactly two main eigenvalues and with pendent vertices are discussed. As an application, we obtain, together with known results, all connected bicyclic and tricyclic graphs with exactly two main eigenvalues.

KW - 2-walk linear graphs

KW - Bicyclic graphs

KW - Main eigenvalues

KW - Tricyclic graphs

UR - http://www.scopus.com/inward/record.url?scp=84863010398&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2011.11.025

DO - 10.1016/j.aml.2011.11.025

M3 - Article

AN - SCOPUS:84863010398

VL - 25

SP - 1274

EP - 1278

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

IS - 10

ER -