International Journal of Mathematics Trends and Technology
Volume 52 | Number 4 | Year 2017 | Article Id. IJMTT-V52P536 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P536
Graph parameters related to Roman military defense strategy were studied by many persons [1, 2, 3, 4, 5, 6]. Satheesh and Sureshkumar introduced Roman labeling and Roman number of graphs [7]. In this paper, we extend this labeling to a new type of labeling called Greek labeling and a related graph parameter, called Greek Number, for a graph. The motivation for Roman and Greek labelings were discussed. Also, its properties are studied and its values for special types of graphs are explored.
[1] J. R. Lewis, Vertex-Edge and Edge-Vertex Parameters in Graphs, Ph.D. Thesis submitted to the Graduate School of Clemson University.
[2]C. S. ReVelle and K. E. Rosing, Defendens imperium Romanum: A classical problem in military strategy, American Mathematical Monthly, (2000), 585 - 594.
[3] D. Ochmanek, Time to restructure U.S defence force, ISSUES in Scienceand Technology, Winter 1996. [4] A. Pagourtzis, P. Penna, K. Schlude, K. Steinhofel, D. S. Tailor and P.Windmayer, Server placements, Roman domination and other dominating set variants, 2nd IFIP International conference on theoretical Computer Science, Montreal (2002), 280 - 291.
[5] K. W. Peters. Theoretical and Algorithmic Results on Domination and Connectivity, Ph.D. thesis, Clemson University, Clemson, SC, 1986.
[6] I. Petersen, Defending Roman Empire, MathTreck, September 11 (2000),www.maa.org.
[7] Satheesh E.N. and J.Suresh Kumar, Roman labelings of Graphs and Application to Military defense, International Journal on Mathematical Trends and Technology (IJMTT), India, November, 2017.
[8] Frank Harary, Graph Theory, Reading mass, 1969
Satheesh E.N, "Greek Labelings of graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 4, pp. 249-252, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P536
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