Thereafter several studies have been dedicated in obtaining variations of the concept. Therefore uv is an edge in G and hence either u or v lies in every minimum vertex covering set of G. Link to Publisher's Version. Hence I itself is a vertex covering transversal dominating set of G. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every graph. So i G is the minimum cardinality of a maximal independent set in G. The authors declare that there are no competing interests regarding the publication of this paper.
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Related article at Pubmed , Scholar Google. Then D is a dominating set of Q 4. The vertices of even weight form an independent set and so do the vertices of odd weight. Let S j and T j be the complement of each I j and J j. A Showcase of scholarship, research, and creativity at the university of southern mississippi. Permanent link to this document https: Publication Title Annals of Combinatorics.
Download Email Please enter a valid email address. Were these topics helpful? For permissions, please e-mail: Journals with no new volumes being added to the archive. Sign In Forgot password? Let G be a simple graph.