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Title: Relations between (κ, τ)-regular sets and star complements
Author: Andelic, M.
Cardoso, Domingos M.
Simic, S. K .
Keywords: Eigenvalue
Star complement
Non-main eigenvalue
Hamiltonian graph
Issue Date: Mar-2013
Publisher: Springer
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 (k ,t)-regular if it induces a k -regular subgraph and every vertex not in the subset has t neighbors in it. We investigate the graphs having a (k,t)-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.
Peer review: yes
DOI: 10.1007/s10587-013-0005-5
ISSN: 0011-4642
Appears in Collections:CIDMA - Artigos

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