Mod sum graph labelling of H m, n and K n .
Martin Sutton, Mirka Miller · 1999
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. 1