|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||Abstract:||
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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