Skolem Difference Mean Graphs

Authors

  • M. Selvi Dr. Sivanthi Aditanar College of Engineering.
  • D. Ramya Dr. Sivanthi Aditanar College of Engineering.
  • P. Jeyanthi Govindammal Aditanar College for Women.

DOI:

https://doi.org/10.4067/S0716-09172015000300004

Keywords:

Mean labeling, Skolem difference mean labeling, Skolem difference mean graph, Extra skolem difference mean labeling.

Abstract

A graph G = (V, E) with p vertices and q edges is said to have
skolem difference mean labeling if it is possible to label the vertices
x ∈ V with distinct elements f(x) from 1, 2, 3, · · · , p+q in such a way
that for each edge e = uv, let f *(e) = l|f(u)- 2 f(v)|m and the resulting
labels of the edges are distinct and are from 1, 2, 3, · · · , q. A graph
that admits a skolem difference mean labeling is called a skolem difference mean graph. In this paper, we prove Cn@Pm(n ≥ 3, m ≥ 1),
T hK1,n1 : K1,n2 : · · · : K1,nmi, T hK1,n1 ◦ K1,n2 ◦ ◦ ◦ K1,nmi,
St(n1, n2, · · · , nm) and Bt(n, n, · · · , n| {z }m times) are skolem difference mean graphs.

Author Biographies

M. Selvi, Dr. Sivanthi Aditanar College of Engineering.

Department of Mathematics.

D. Ramya, Dr. Sivanthi Aditanar College of Engineering.

Department of Mathematics.

P. Jeyanthi, Govindammal Aditanar College for Women.

Research Centre, Department of Mathematics.

References

[1] F. Harary, Graph theory, Addison Wesley, Massachusetts, (1972).

[2] Joseph A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, 17 (2014), # DS6.

[3] K. Murugan and A. Subramanian, Skolem difference mean labeling of H-graphs, International Journal of Mathematics and Soft Computing, Vol.1, No. 1, pp. 115-129, (2011).

[4] K. Murugan and A. Subramanian, Labeling of subdivided graphs, American Journal of Mathematics and Sciences, Vol.1, No. 1, pp. 143-149, (2012).

[5] K. Murugan and A. Subramanian, Labeling of finite union of paths, International Journal of Mathematics and Soft Computing, Vol.2, No. 1, pp. 99-108, (2012).

[6] D. Ramya, M. Selvi and R. Kalaiyarasi, On skolem difference mean labeling of graphs, International Journal of Mathematical Archive, 4(12), pp. 73-79, (2013).

[7] D. Ramya and M. Selvi, On skolem difference mean labeling of some trees, International Journal of Mathematics and Soft Computing, Vol.4, No. 2, pp. 11-18, (2014).

[8] S. Somasundaram and R. Ponraj, Mean labelings of graphs, National Academy Science Letter, 26, pp. 210-213, (2003).

How to Cite

[1]
M. Selvi, D. Ramya, and P. Jeyanthi, “Skolem Difference Mean Graphs”, Proyecciones (Antofagasta, On line), vol. 34, no. 3, pp. 243-254, 1.

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Artículos