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Open Access Research Article

Odd vertex even edge root square mean labelling graphs

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pp. 1001–1008Vol. 27Issue 5August 2024DOI: 10.47974/JIM-1923XML
Received:
05 Mar 2024
Published Online:
30 Aug 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-1923
Pages:
1001–1008

Abstract

Let G be a graph with p-vertices and q edges. A graph G is said to be odd vertex even edge root square mean labelling if there exist an injective map f : V(G)→{1, 2, 3…..2q+1} such that the induced edge labels are even and distinct which can be obtained by f *(e) = √(f(u)2+f(v)2/2  or √f(u)2+f(v)2)/2. A graph that allows such labelling is called an odd vertex even edge root square mean labelling graph. This paper introduces this new labelling type and discusses several related theorems concerning path graphs.

Keywords

Subject Classifications

(2010) 05C78

References

[1] J.A.Gallian, ‘A dynamic survey of graphs labelling’,The electronic journal  of combinatorics,18 (2015).
[2] B.Gayathri and R.Gobi, ‘(k, d) even mean labelling of corona graphs, International Journal of Mathematics and Soft Computing, Vol.(1), 17-23, Aug (2011).
[3] B.Gayathri and R.Gobi, ‘Necessary condition for mean labelling, International Journal of Engineering Science, Advanced Computing and Bio Technology’, Vol. 4(3), 43-52, July-Sep. (2013).
[4] R.Ramdani, A.Y Fanisa, S. Gumilar, S Sabini, ‘Root square Mean labelling of some graphs obtained from paths ‘ Journal of Physics Conference Series (2021).
[5] S.Somasundaram and R.Ponraj, ‘Mean labelling of graphs’, National academy science letters, 26, 210-213 (2003). 
[6] S. Sandiya, S. Somasundaram and S.Arun,‘Root square mean labelling graphs’ Internal Journal Contemporary Math. Science, Vol.9(14),  page no. 667-676 (2014).
[7] K. Thirugnasambandam and K. Venkatesan,’ Super root square mean labelling of graphs’, International Journal of Mathematics and Soft Computing, Vol. 5(2), page no. 189-198 (2025).
[8] Senthilkumar.V, Ponnappan. C.Y., and Selvam. A., A note on Domination in fuzzy graph G(σ, µ) using Strong arc, Journal of Science and Computation, Vol. 5(6), page. no. 84-92 (2018).
[9] Senthilkumar.V, Ponnappan. C.Y., Note on strong support vertex covering of  fuzzy graph G(σ ,µ)  by  strong arc, Advances and applications in Mathematics, Mili  publication, Vol. 18, issue 11 (2019).
[10] Senthilkumar.V, Ponnappan. C.Y.,Introduction to strong support dominationin fuzzy graphs by strong arc, Advances in Mathematics: Scientific Journal 8, no. 3, 724- 735 (2019).
[11]  Senthilkumar.V, Global strong domination in α- Cut diminish fuzzy graph by α- Cut strong arc.  Bulletin of pure and Applied Sciences-E Maths & Statistics,.Vol.41E (1), Page 81-87 June (2022).
[12] Ponnappan, C.Y., Senthilkumar.V., Domination in Cartesian product fuzzy graphs by Strong arc, Bulletin of pure and applied mathematics,Vol(2), 37E (Math& Stat), 321-336 (2018).
[13] Ponnappan, C.Y., Senthilkumar.V., Case study of non- strong arc in Cartesian product fuzzy graphs, Annls of Pure and Applied Mathematics, Vol. 18, no 1, 15-25, July (2018).
[14] Ponnappan, C.Y., Senthilkumar.V.,  Study of Domination in(Union and Join) of fuzzy graphs, Mathematical Sciences International Research Journal, volume 7, issue 2, IMRF journal publication, Sep. (2018).
[15] Senthilkumar. V., Types of Domination in Intuitionistic fuzzy graph by strong arc an effevtive  arc. Bulletin of pure and applied mathematics,Vol (2), 37E (Math& Stat), 490-498 (2018).
[16] Ponnappan, C.Y., Senthilkumar., A selvam , A note on intuitionistic fuzzy graph by strong arc, JASC, Vol 5 (3) 957-968, March (2019).
[17] Senthilkumar.V, Ponnappan. C.Y, Independent strong support domination& Independent anti – strong support domination in fuzzy graphs by strong Arc, Advances  in Mathematics : Scientific  Journal 8, no. 3, 714-723 (2019).

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