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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 7 | Year 2020 | Article Id. IJMTT-V66I7P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I7P502

Some Results On κ -Relaxed Mean Graphs


R. Thayalarajan
Abstract

A graph G = (V,E) with p vertices and q edges is said to be a κ-relaxed mean graph if there exists a function f from the vertex set of G to {k-1,k,k+1,k+2,..., k + q} such that in the induced map f* from the edge set of G to { k, k+1,k+2,..., k+q-1} defined by f*(e =uv) = { f(u)+f(v)/2 iff(u)+f(v) is even, f(u)+f(v)+1/2 if f(u( +f(v) is odd. the resulting edge labels are distinct. In this paper, we prove some results on k-relaxed mean labeling of some graphs.

Keywords
κ-relaxed mean labeling (κ-RML), κ-relaxed mean graph( κ-RMG).
References

[1] Frank Harary, “Graph Theory”, Narosa Publishing House (2001).
[2] Gayathri. B and Thayalarajan. R, “Variations and Extensions of Mean labeling”, Bharathidasan University, Ph.D., Thesis (October 2018), pp.1-224.
[3] Gallian J.A, “A dynamic survey on graph labeling”, The Electronnics Journal of Combinatorics, (2019) #DS6.
[4] V.Maheswari, D.S.T.Ramesh and V.Balaji, “Relaxed mean labeling”, International Journal of Mathematics Research, Volume 4, 3 (2012), 217-224.
[5] V. Maheswari, D.S.T. Ramesh and V. Balaji, “ Some results on relaxed mean labeling”, International J.Math. Combin., Vol.3(2015), pp.73-80.
[6] Somasundaram. S and Ponraj. R, “Mean Labeling of Graphs”, National Academy Science Letters, 26(2003), pp.210-213.
[7] S.Somasundaram and R.Ponraj, “Some results on mean graphs”, Pure and Applied Mathematika Sciences, 58(2003), 29 – 35.

Citation :

R. Thayalarajan, "Some Results On κ -Relaxed Mean Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 7, pp. 8-17, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I7P502

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