Radio Geometric Mean Labeling of Some Star Like Graphs

Authors

  • V. Hemalatha Department of Mathematics, Vivekanandha College of Technology for Women, Tiruchengode
  • V. Mohanaselvi PG and Research Department of Mathematics, Nehru Memorial College, Puthanampatti
  • K. Amuthavalli PG and Research Department of Mathematics, Govt. Arts and Science College, Ariyalur

DOI:

https://doi.org/10.26713/jims.v9i3.1017

Keywords:

Radio Geometric Mean labeling, Star, Bistar, Diameter, Lotus inside a circle, \(k\)-ary tree

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.

Downloads

Download data is not yet available.

References

G. Chartrand, D. Erwin, P. Zhang and F. Harary, Radio labeling of graphs, Bull. Inst. Combin. Appl. 33 (2001), 77 – 85.

R. Kchikech, M. Khennoufa and O. Togni, Linear and cyclic radio k-labelings of trees, Discuss. Math. Graph Theory 130(3) (2007), 105 – 123.

R. Kchikech, M. Khennoufa and O. Togni, Radio k-labelings for Cartesian products of graphs, Discuss. Math. Graph Theory 28(1) (2008), 165 – 178.

M. Khennoufa and O. Togni, The radio antipodal and radio numbers of the hypercube, Ars Combin. 102 (2011), 447 – 461.

D. Liu, Radio number for trees, Discrete Math. 308(7) (2008), 1153 – 1164.

D. Liu and X. Zhu, Multilevel distance labeling for paths and cycles, SIAM J. Discrete Math. 19(3) (2005), 610 – 621.

D. Liu and M. Xie, Radio number for square of cycles, Congr. Numer. 169 (2004), 105 – 125.

D. Liu and M. Xie, Radio number for square of paths, Ars Combin. 90 (2009), 307 – 319.

D. Liu and R.K. Yeh, On distance two labeling of graphs, Ars Combin. 47 (1997), 13 – 22.

R. Ponraj, S. Sathish Narayanan and R. Kala, Radio mean labeling of a graph, AKCE International Journal of Graphs and Combinatorics 12 (2015), 224 – 228.

R. Ponraj, S. Sathish Narayanan and R. Kala, On radio mean number of graphs, International J. Math. Combin. 3 (2014), 41 – 48.

F. Harary, Graph Theory, Addison Wesley, New Delhi (1969).

J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 19 (2012), #DS6.

Downloads

Published

2017-10-30
CITATION

How to Cite

Hemalatha, V., Mohanaselvi, V., & Amuthavalli, K. (2017). Radio Geometric Mean Labeling of Some Star Like Graphs. Journal of Informatics and Mathematical Sciences, 9(3), 969–977. https://doi.org/10.26713/jims.v9i3.1017

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.