International Journal of Mathematics Trends and Technology
Volume 58 | Number 2 | Year 2018 | Article Id. IJMTT-V58P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V58P514
A Radio Mean D-distance labeling of a connected graph G is an injective map f from the vertex set V(G) to โ such that for two distinct vertices u and v of G, d D (u, v) + ๐ ๐ข +๐(๐ฃ) 2 โฅ 1 + diam D (G), where d D (u, v) denotes the D-distance between u and v and diam D (G) denotes the D-diameter of G. The radio mean Ddistance number of f, rmn D (f) is the maximum label assigned to any vertex of G. The radio mean D-distance number of G, rmn D (G) is the minimum value of rmn D (f) taken over all radio mean D-distance labeling f of G. In this paper we find the radio mean D-distance number of graph obtained from graph operation.
[1] F.Buckley and F. Harary, Distance in Graphs,Addition- Wesley, Redwood City, CA, 1990.
[2] G.Chartrand, D. Erwinn, F. Harary, and P. Zhang, โRadio labeling of graphs,โ Bulletin of the Institute of Combinatorics and Its Applications, vol. 33, pp. 77โ85, 2001.
[3] G.Chartrand, D. Erwin, and P. Zhang, Graph labeling problem suggested by FM channel restrict ions, Bull. Inst. Combin. Appl., 43, 43-57(2005).
[4] C.Fernandaz, A. Flores, M. Tomova, and C. Wyels, The Radio Number of Gear Graphs, arXiv:0809. 2623, September 15, (2008).
[5] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 19 (2012) #Ds6.
[6] W.K. Hale, Frequency assignment: Theory and applications, Proc. IEEE 68 (1980), pp.1497โ1514.
[7] F.Harary, Graph Theory, Addision wesley, New Delhi (1969).
[8] R.Khennoufa and O. Togni, The Radio Antipodal and Radio Numbers of the Hypercube, accepted in 2008 publication in ArsCombinatoria.
[9] D.Liu, Radio number for trees, Discrete Math. 308 (7) (2008) 1153โ1164.
[10] D.Liu, X. Zhu, Multilevel distance labelings for paths and cycles, SIAM J. Discrete Math. 19 (3) (2005) 610โ621.
[11] P.Murtinez, J. OrtiZ, M. Tomova, andC. Wyles, Radio Numbers For Generalized Prism Graphs, Kodai Math. J., 22,131-139(1999).
[12] T.Nicholas and K.John Bosco , Radio D-distance number of some graphs, International Journal of Engineering & Scientific Research Vol.5 Issue 2, February 2017, ISSN: 2347-6532.
[13] T.Nicholas, K.John Bosco and M. Antony, Radio mean D-distance labeling of some graphs, International Journal of Engineering & Scientific Research Vol.5 Issue 2, February 2017, ISSN: 2347-6532.
[14] R.Ponraj, S.Sathish Narayanan and R.Kala, Radio mean labeling of graphs, AKCE International Journal of Graphs and Combinatorics 12 (2015) 224โ228.
[15] R.Ponraj, S.Sathish Narayanan and R.Kala, On Radio Mean Number of Some Graphs, International J.Math. Combin. Vol.3(2014), 41-48.
[16] R.Ponraj, S.Sathish Narayanan and R.Kala, Radio Mean Number Of Some Wheel Related Graphs, Jordan Journal of Mathematics and Statistics (JJMS) 7(4), 2014, pp.273 โ 286.
[17] M.T. Rahim, I. Tomescu, OnMulti-level distance labelings of Helm Graphs, accepted for publication in Ars Combinatoria.
[18] Reddy Babu, D., Varma, P.L.N., Average D-Distance Between Edges Of A Graph ,Indian Journal of Science and Technology, Vol 8(2), 152โ156, January 2015.
[19] Reddy Babu, D., Varma, P.L.N.,Average D-Distance Between Vertices Of A Graph, Italian Journal Of Pure And Applied Mathematics - N. 33ยก2014 (293ยก298).
[20] Reddy Babu, D., Varma, P.L.N., D-distance in graphs, Golden Research Thoughts, 2(2013), 53-58.
[21] M.M. Rivera, M. Tomova, C. Wyels, and A. Yeager, The Radio Number of Cn โกCn,re- submitted to Ars Combinatoria, 2009.
T. Nicholas, K. John Bosco, V.Viola, "On Radio Mean D-Distance Number of Graph Obtained from Graph Operation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 58, no. 2, pp. 98-106, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V58P514
PDF 
Abstract 
Keywords 
References 
Citation