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Solution to some open problems on E-super vertex magic labeling of disconnected graphs

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  • Marimuthu, Gurusamy Thevar
  • Kumar, Gurunathan

Abstract

An E-super vertex magic labeling is a bijection f :V(G)UE(G)→{1,2,3,…,p+q} such that for each vertex u, f(u)+∑v∈N(u)f(uv)=k for some constant k where f(E(G))={1,2,3,…,q}. A graph that admits an E-super vertex magic labeling is called an E-super vertex magic graph. The only disconnected graphs that have been shown to be E-super vertex magic are mCn if and only if both m and n are odd. The article “Marimuthu and Balakrishnan (2012)” discussed the E-super vertex magicness of connected graphs. In this paper, we pay our attention to prove the existence and non existence of E-super vertex magic labeling for some families of disconnected graphs. Also we provide solution to some open problems found in the article “Gray and MacDougall (2009)”.

Suggested Citation

  • Marimuthu, Gurusamy Thevar & Kumar, Gurunathan, 2015. "Solution to some open problems on E-super vertex magic labeling of disconnected graphs," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 657-663.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:657-663
    DOI: 10.1016/j.amc.2015.06.096
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