Radio Square Difference Dd-Distance Number of
Some Basic Graphs

K. John Bosco; G. Vishma George

doi:https://doi.org/10.14445/22315373/IJMTT-V67I2P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 2 | Year 2021 | Article Id. IJMTT-V67I2P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I2P515

Radio Square Difference Dd-Distance Number of Some Basic Graphs

K. John Bosco, G. Vishma George

Citation :

K. John Bosco, G. Vishma George, "Radio Square Difference Dd-Distance Number of Some Basic Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 2, pp. 109-113, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I2P515

Abstract

A Radio square difference Dd-distance labeling of a connected graph 𝐺 is an injective function 𝑓 from the vertex set 𝑉(𝐺) to N such that for two distinct vertices 𝑢 and 𝑣 of 𝐺, 𝐷 𝐷𝑑(𝑢, 𝑣) + |[𝑓(𝑢)] 2 − [𝑓(𝑣)] 2 | ≥ 1 + 𝑑𝑖𝑎𝑚𝐷𝑑(𝐺), where 𝐷 𝐷𝑑(𝑢, 𝑣) denote the Dd-distance between 𝑢 and 𝑣 and also 𝑑𝑖𝑎𝑚𝐷𝑑(𝐺)denotes the Dd-diameter of 𝐺.The radio square difference number of 𝑓, 𝑟𝑠𝑑𝑛𝐷𝑑(𝑓) is the maximum label assigned to any vertex of 𝐺. The radio square difference number of 𝐺, 𝑟𝑠𝑑𝑛𝐷𝑑(𝐺) is the maximum value of 𝑓 of 𝐺. In this paper we find the radio square difference number of some basic graph.

Keywords

Dd-distance, Radio square.

References

[1] F. Buckley and F. Harary , Distance in Graphs , Addition- Wesley, Redwood City, CA, 1009.
[2] G .Chatrand, D.Erwinn, F .Harary , and P. Zhang, Radio labelling of graphs, Bulletin of the Institute of Combinatorics and its Applications 33(2001) 77-85.
[3] G .Chatrand, D. Erwin, and P. Zhang, Graph labeling problem suggested by FM channel restrictons, Bull. Inst. Combin.Appl.,43(2005) 43-57.
[4] C. Fernandaz, A. Flores, M. Tomova, and C.Wyels, The Radio Number of Gear Graphs ,arXiv:0809.2623, 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) 1497-1514.
[7] J. Shiama, Square difference labelling for some graphs, International journal of Computer Applications (0975-08887) 44(4)(2012).
[8] Anto Kinsley and Siva Ananthi P, Dd- Distance in Graphs, Imperical Journal of Interdisciplinary Research (IJIR), 3(2) (2017) ISSN:2454-1362, http://www.onlinejournal.in
[9] T.Nicholas and K.John Bosco , Radio D-distance number of some graphs, International Journal of Engineering & Scientific Research 5(2)(2017) ISSN: 2347-6532.
[10] T.Nicholas, K.John Bosco and M. Antony, Radio mean D-distance labeling of some graphs, International Journal of Engineering & Scientific Research 5(2)(2017) ISSN: 2347-6532. publication in Ars Combinatoria.
[11] K.John bosco,G.Vishma George, On Radio square Difference D-distance number of some standard graphs, IJRAR 8(1)(2021) www.ijrar.org (E-ISSN 2348-1269, P- ISSN 2349-5138)
[12] K.John bosco, G.Vishma George, On Radio square difference Dd-distance number of cycle related Graphs, JETIR 8(1) (2021) www.jetir.org (ISSN-2349-5162)
[13] Reddy Babu, D., Varma, P.L.N., D-distance in graphs, Golden Research Thoughts, 2(2013) 53-58.