Mod sum graph labelling of Hm, n and Kn

@article{Sutton1999ModSG,
  title={Mod sum graph labelling of Hm, n and Kn},
  author={Martin Sutton and Mirka Miller},
  journal={Australasian J. Combinatorics},
  year={1999},
  volume={20},
  pages={233-240}
}
The mod sum number p( G) of a connected graph G is the minimum number of isolated vertices required to transform G into a mod sum graph. It is known that the mod sum number is greater than zero for wheels, Wn, when n > 4 and for the complete graphs, Kn when n 2: 2. In this paper we show that p( Hm,n) > 0 for n > m ;::: 3. Vie show further that P(K2) = P(K3) = 1 while p(Kn) = n for n ;::: 4. We thus provide for the first time q,n exact nonzero mod sum number for an infinite class of graphs.