On Harmonious Labelings of the Balanced Quintuple Shells

Part of the Communications in Computer and Information Science book series (CCIS, volume 236)


A multiple shell MS {n1t1, n2t2 ,. . . , nr tr } is a graph formed by ti shells of widths n i , 1 ≤ ir, which have a common apex. This graph has \(\sum^{r}_{i=1}\) ti(ni–1)+1 vertices. A multiple shell is said to be balanced with width w if it is of the form MS{w s } or MS{(w + 1) t , w s }. Deb and Limaye have conjectured that all multiple shells are harmonious. The conjecture has been shown true for the balanced double shells, the balanced triple shells and the balanced quadruple shells. In this paper, the conjecture is proved to be true for the balanced quintuple shells.


harmonious graph multiple shell vertex labeling edge labeling 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xi Yue
    • 1
  1. 1.School of Computer ScienceWuyi UniversityJiangmenP.R. China

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