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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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Open Access
Online
ISSN
2391-5455
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Volume 11, Issue 10

Issues

Volume 13 (2015)

Tricyclic graphs with exactly two main eigenvalues

Xiaoxia Fan / Yanfeng Luo / Xing Gao
Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0283-z

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.

MSC: 05C50

Keywords: Main eigenvalues; Tricyclic graphs; 2-walk (a; b)-linear graphs

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About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01


Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1800–1816, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0283-z.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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