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dc.contributor.authorAnđelić, Milicapt_PT
dc.contributor.authorCardoso, Domingos M.pt_PT
dc.contributor.authorSimić, Slobodan K.pt_PT
dc.contributor.authorStanić, Zoranpt_PT
dc.description.abstractA vertex v ∈ V (G) is called λ-main if it belongs to a star set X ⊂ V (G) of the eigenvalue λ of a graph G and this eigenvalue is main for the graph obtained from G by deleting all the vertices in X \ {v}; otherwise, v is λ-non-main. Some results concerning main and non-main vertices of an eigenvalue are deduced. For a main eigenvalue λ of a graph G, we introduce the minimum and maximum number of λ-main vertices in some λ-star set of G as new graph invariant parameters. The determination of these parameters is formulated as a combinatorial optimization problem based on a simplex-like approach. Using these and some related parameters we develop new spectral tools that can be used in the research of the isomorphism problem. Examples of graphs for which the maximum number of λ-main vertices coincides with the cardinality of a λ-star set are provided.pt_PT
dc.subjectMain eigenvaluept_PT
dc.subjectMain vertexpt_PT
dc.subjectStar set and main star setpt_PT
dc.subjectIsomorphism problempt_PT
dc.titleThe main vertices of a star set and related graph parameterspt_PT
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