Authors: Andelić, Milica
Cardoso, Domingos
Simić, Slobodan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Relations between (κ, τ)-regular sets and star complements
Journal: Czechoslovak Mathematical Journal
Volume: 63
Issue: 1
First page: 73
Last page: 90
Issue Date: 2-Apr-2013
Rank: M23
ISSN: 0011-4642
DOI: 10.1007/s10587-013-0005-5
Let G be a finite graph with an eigenvalue μ of multiplicity m. A set X of m vertices in G is called a star set for μ in G if μ is not an eigenvalue of the star complement G\X which is the subgraph of G induced by vertices not in X. A vertex subset of a graph is (κ, τ)-regular if it induces a κ-regular subgraph and every vertex not in the subset has τ neighbors in it. We investigate the graphs having a (κ, τ)-regular set which induces a star complement for some eigenvalue. A survey of known results is provided and new properties for these graphs are deduced. Several particular graphs where these properties stand out are presented as examples.
Keywords: eigenvalue | Hamiltonian graph | non-main eigenvalue | star complement
Publisher: Springer Link
Project: FCT - Fundação para a Ciência e a Tecnologia, Project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690 and Project PTDC/MAT/112276/2009
Graph theory and mathematical programming with applications in chemistry and computer science 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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