On SD-Harmonious Labeling
DOI:
https://doi.org/10.12723/mjs.46.1Keywords:
SD-harmonious labelingAbstract
A graph G is said to be SD-harmonious labeling if there exists an injection f: V(G) -> {0,1,2,...,q} such that the induced function f*: E(G) ->{0,2,...,2q-2} defined by f(uv)=S+D (mod 2q) is bijective, where S=f(u)+f(v) and D=|f(u)-f(v)|, for every edge uv in E(G). A graph which admits SD-harmonious labeling is called SD-harmonious graph. In this paper, we investigate SD-harmonious labeling of path related graphs, tree related graphs, star related graphs and disjoint union of graphs.
References
[1] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, MacMillan, New York, 1976.
[2] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs International Symposium, Rome, 1966.
[3] J. A. Gallian, “A Dyamic Survey of Graph Labeling”, The Electronic J. Combin., vol. 20, # DS6, 2017.
[4] R. L. Graham and N. J. A. Sloane, “On additive bases and harmonious graphs”, SIAM J. Algebr. Discrete Methods, vol. 1, pp. 382-404, 1980.
[5] G. C. Lau and W. C. Shiu, “On SD-prime labeling of graphs”, Utilitas Math., (accepted).
[6] G. C. Lau, W. C. Shiu, H. K. Ng, C. D. Ng and P. Jeyanthi, “Further results on SD-prime labeling”, JCMCC, vol. 98, pp. 151-170, 2016.
[7] G. C. Lau, W. C. Shiu and H. K. Ng, “Further results on super graceful labeling of graphs”, AKCE International Journal of Graphs and Combinatorics, vol. 13, pp. 200-209, 2016.
[8] M. A. Perumal, S. Navaneethakrishnan, S. Arockiaraj and A. Nagarajan, “Super graceful labeling for some special graphs”, Int. J. Res. Rev. Appl. Sci., vol. 9, no.3, pp. 382-404, 2011.
[9] D. Stewart, Even harmonious labelings of disconnected graphs (Master’s thesis), University of Minnesota Duluth, 2015.
[10] V. Swaminathan and P. Jeyanthi, “Super edge-magic strength of fire cracker, banana trees and unicycle graphs”, Discrete Mathematics, vol. 306 pp. 1624-1636, 2006.
[2] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs International Symposium, Rome, 1966.
[3] J. A. Gallian, “A Dyamic Survey of Graph Labeling”, The Electronic J. Combin., vol. 20, # DS6, 2017.
[4] R. L. Graham and N. J. A. Sloane, “On additive bases and harmonious graphs”, SIAM J. Algebr. Discrete Methods, vol. 1, pp. 382-404, 1980.
[5] G. C. Lau and W. C. Shiu, “On SD-prime labeling of graphs”, Utilitas Math., (accepted).
[6] G. C. Lau, W. C. Shiu, H. K. Ng, C. D. Ng and P. Jeyanthi, “Further results on SD-prime labeling”, JCMCC, vol. 98, pp. 151-170, 2016.
[7] G. C. Lau, W. C. Shiu and H. K. Ng, “Further results on super graceful labeling of graphs”, AKCE International Journal of Graphs and Combinatorics, vol. 13, pp. 200-209, 2016.
[8] M. A. Perumal, S. Navaneethakrishnan, S. Arockiaraj and A. Nagarajan, “Super graceful labeling for some special graphs”, Int. J. Res. Rev. Appl. Sci., vol. 9, no.3, pp. 382-404, 2011.
[9] D. Stewart, Even harmonious labelings of disconnected graphs (Master’s thesis), University of Minnesota Duluth, 2015.
[10] V. Swaminathan and P. Jeyanthi, “Super edge-magic strength of fire cracker, banana trees and unicycle graphs”, Discrete Mathematics, vol. 306 pp. 1624-1636, 2006.
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Published
2018-07-01
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Research Articles
