On eigenvalue inequalities of a matrix whose graph is bipartite
نویسندگان
چکیده
منابع مشابه
On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle
We consider the general problem of determining the maximum possible multiplicity of an eigenvalue in a Hermitian matrix whose graph contains exactly one cycle. For some cases we express that maximum multiplicity in terms of certain parameters associated with the graph. © 2006 Elsevier Inc. All rights reserved. AMS classification: 15A18; 05C38; 05C50
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A different approach is given to recent results due mainly to R.C. Johnson and A. Leal Duarte on the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree. The technics developed are based on some results of matchings polynomials and use a work by O.L. Heilmann and E.H. Lieb on an apparently unrelated topic.
متن کاملSome Inequalities For The Largest Eigenvalue Of A Graph
Combinatorics, Probability & Computing / Volume 11 / Issue 02 / March 2002, pp 179 189 DOI: 10.1017/S0963548301004928, Published online: 25 April 2002 Link to this article: http://journals.cambridge.org/abstract_S0963548301004928 How to cite this article: V. NIKIFOROV (2002). Some Inequalities for the Largest Eigenvalue of a Graph. Combinatorics, Probability & Computing, 11, pp 179-189 doi:10.1...
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In this paper, we determine the unique graph whose least signless Laplacian eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with maximum degree Δ and among all non-bipartite connected graphs of order n with maximum degree Δ, respectively.
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2019
ISSN: 1029-242X
DOI: 10.1186/s13660-019-2001-2