Radio Geometric Mean Labeling of Some Star Like Graphs (Journal of Informatics and Mathematical Sciences, 2017)
A radio Geometric Mean Labeling of a connected graph \(G\) is a one to one map \(f\) from the vertex set \(V(G)\) to the set of natural numbers \(N\) such that for two distinct vertices \(u\) and \(v\) of \(G\), \(d\left(u,v\right)+\left\lceil \sqrt{f(u)f(v)} \right\rceil \ge 1+diam(G)\). The radio geometric mean number of \(f,\, r_{gmn} (f)\) is the maximum number assigned to any vertex of \(G\). The radio geometric mean number of \(G\), \(r_{gmn} (G)\) is the minimum value of \(r_{gmn} (f)\) taken over all radio geometric mean labeling \(f\) of \(G\). In this paper, we find the radio geometric mean number of some star like graphs.
Keywords: Radio Geometric Mean labeling; Star; Bistar; Diameter; Lotus inside a circle; \(k\)-ary tree