Publication

Abstract : A one-one mapping f : V (G) → Z+ satisfying the condition $d(u,v) + \left[ {\sqrt {f(u){\rm{f}}(v)} } \right] \ge diam(G) + 1$, for every pair of distinct vertices in G is defined as radio geometric mean labeling of G. The maximum number assigned to any vertex of G under the labeling f is called its radio geometric mean number of f denoted rgmn(f). The least value of rgmn(f), taken over all such labelings f of G is defined as its radio geometric mean number and is denoted by rgmn(G). Clearly, rgmn(G) ≥ |V(G)|. Graphs for which rgmn(G) = |V(G)| are defined as radio geometric graceful. In this paper, we find the radio geometric mean number of certain classes of graphs like sunflowers, Helms, gear graphs and show that they are radio geometric graceful.