Strongly *- labeling

S. Teresa Arockiamary; J. Maria Angelin Visithra

doi:https://doi.org/10.14445/22315373/IJMTT-V63P510

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 63 | Number 1 | Year 2018 | Article Id. IJMTT-V63P510 | DOI : https://doi.org/10.14445/22315373/IJMTT-V63P510

Strongly *- labeling

S. Teresa Arockiamary, J. Maria Angelin Visithra

Abstract

A graph G =(V,E) is said to be strongly *-graph if there exists a bijection 𝑓: 𝑉 → {1,2, … , 𝑛} in such a way that when an edge, whose end vertices are labeled i and j, is labeled with the value i+j+ij , all edge labels are distinct. In this paper we prove that < 𝐾1,𝑛 (1) : 𝐾1,𝑛 (2) >, < 𝐾1,𝑛 (1) : 𝐾1,𝑛 (2) : …: 𝐾1,𝑛 (𝑘) >, < 𝐾1,𝑛 (1) : 𝐾1,𝑛 (2) > with cycle and < 𝐾1,𝑛 (1) : 𝐾1,𝑛 (2) : …: 𝐾1,𝑛 (𝑘) > with cycle are strongly *- graph.

Keywords

Labeling, strongly *- labeling, strongly *- graph, star graph.

References

[1] C. Adiga and D. Somashekara, Strongly *-graphs, Math. Forum, Volume 13, 31-36, 1999/2000.
[2] J. Baskar Babujee and V. Vishnupriya, Permutation labelings for some trees, Internat. J. Math. Comput. Sci., Volume 3, 31-38, 2008.
[3] J. Baskar Babujee and C. Beaula, On vertex strongly *-graph, Proced. Internat. Conf. Math. and Comput. Sci., 25-26, July 2008.
[4] J. Baskar Babujee, K. Kannan and V. Vishnupriya, Vertex Strongly *-graphs, Internat. J. Analyzing Components and Combin. Biology in Math., Volume 2, 19-25.
[5] Gallian J.A, A Dynamic Survey of graph labeling, The Electronic Journal of Combinatorics, 20th edition, (2017).
[6] M. A. Seoud and A. E. A. Mahran, Necessary conditions for strongly *-graphs, AKCE Int. J. Graphs Comb., Volume 9, 115-122, 2012.

Citation :

S. Teresa Arockiamary, J. Maria Angelin Visithra, "Strongly *- labeling," International Journal of Mathematics Trends and Technology (IJMTT), vol. 63, no. 1, pp. 75-81, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V63P510