Radio Geometric Mean Labeling of Some Star Like Graphs

V. Hemalatha, V. Mohanaselvi, K. Amuthavalli

Abstract


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 \(G\), \(d\left(u,v\right)+\left\lceil \sqrt{f(u)f(v)} \right\rceil \ge 1+\mathrm{diam}(G)\). 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

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v9i3.1017

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