P. K. Deb and N. B. Limaye [Ars Comb. 65, 155–176 (2002; Zbl 1071.05567)] have conjectured that all multiple shells are harmonious, and shown that the ...

This graph has ∑ i = 1 r ti(ni–1)+1 vertices. A multiple shell is said to be balanced with width w if it is of the form MS{ws} or MS{(w + 1)t, ws}. Deb and ...

In this paper, the conjecture is proved to be true for the balanced quintuple shells and the balanced double shells, the balanced triple shells, and balanced ...

Mar 14, 2018 · Bibliographic details on On Harmonious Labelings of the Balanced Quadruple Shells.

Yang et al. [11] proved the conjecture is true for balanced quadruple shells. In 2011, Yue [10] has proved that "balanced quintuple shells are harmonious". ...

On Harmonious Labelings of the Balanced Quadruple Shells · Yuansheng Yang ... balanced quadruple shells and is proved to be true forThe balanced quintuple shells.

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the mid.

The planar Ramsey number PR(K4-e, K5). Discret. Math. 307(1): 137-142 (2007) ... On Harmonious Labelings of the Balanced Quadruple Shells. Ars Comb. 75 (2005) ...

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the mid.