• Title/Summary/Keyword: vertex out-magic total labeling

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V-SUPER VERTEX OUT-MAGIC TOTAL LABELINGS OF DIGRAPHS

  • Devi, Guruvaiah Durga;Durga, Morekondan Subhash Raja;Marimuthu, Gurusamy Thevar
    • Communications of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.435-445
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    • 2017
  • Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a bijection f from $V(D){\cup}A(D){\rightarrow}\{1,2,{\ldots},p+q\}$ with the property that for every $v{\in}V(D)$, $f(v)+\sum_{u{\in}O(v)}f((v,u))=k$, for some constant k. Such a labeling is called a V-super vertex out-magic total labeling (V-SVOMT labeling) if $f(V(D))=\{1,2,3,{\ldots},p\}$. A digraph D is called a V-super vertex out-magic total digraph (V-SVOMT digraph) if D admits a V-SVOMT labeling. In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such labelings for digraphs. In particular, we completely solve the problem of finding V-SVOMT labeling of generalized de Bruijn digraphs which are used in the interconnection network topologies.