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A study on the product set-labeling of graphs

  • Sudev Naduvath EMAIL logo
Veröffentlicht/Copyright: 20. Januar 2017
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Abstract

Let X be a non-empty ground set and 𝒫(X) be its power set. A set-labeling (or a set-valuation) of a graph G is an injective set-valued function f:V(G)𝒫(X) such that the induced function f:E(G)𝒫(X) is defined by f(uv)=f(u)f(v), where f(u)f(v) is a binary operation of the sets f(u) and f(v). A graph which admits a set-labeling is known to be a set-labeled graph. A set-labeling f of a graph G is said to be a set-indexer of G if the associated function f is also injective. In this paper, we introduce a new notion, namely, product set-labeling of graphs as an injective set-valued function f:V(G)𝒫() such that the induced edge-function f:V(G)𝒫() is defined as f(uv)=f(u)f(v) for all uvE(G), where f(u)f(v) is the product set of the set-labels f(u) and f(v), where is the set of all positive integers and discuss certain properties of the graphs which admit this type of set-labeling.

MSC 2010: 05C78

Acknowledgements

The author would like to dedicate this work to Professor (Dr.) T. Thrivikraman, who has been his mentor, motivator and the role model in teaching as well as in research.

References

[1] Acharya B. D., Set-Valuations and Their Applications, MRI Lecture Notes Appl Math. 2, The Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad, 1983. Suche in Google Scholar

[2] Bondy J. A. and Murty U. S. R., Graph Theory with Application, North-Holland, New York, 1982. Suche in Google Scholar

[3] Gallian J. A., A dynamic survey of graph labelling, Electron. J. Combin. 2015 (2015), Paper No. DS-6. Suche in Google Scholar

[4] Germina K. A. and Sudev N. K., On weakly uniform integer additive set-indexers of graphs, Int. Math. Forum 8 (2013), no. 37, 1827–1834. 10.12988/imf.2013.310188Suche in Google Scholar

[5] Harary F., Graph Theory, New Age International, New Delhi, 2002. Suche in Google Scholar

[6] Nathanson M. B., Additive Number Theory, Inverse Problems and Geometry of Sumsets, Springer, New York, 1996. 10.1007/978-1-4757-3845-2Suche in Google Scholar

[7] Sudev N. K. and Germina K. A., On certain arithmetic integer additive set-indexers of graphs, Discrete Math. Algorithms Appl. 7 (2015), no. 3, 1–15. 10.1142/S1793830915500251Suche in Google Scholar

[8] Sudev N. K. and Germina K. A., Some new results on strong integer additive set-indexers of graphs, Discrete Math. Algorithms Appl. 7 (2015), no. 1, 1–11. 10.1142/S1793830914500657Suche in Google Scholar

[9] Sudev N. K. and Germina K. A., A study on arithmetic integer additive set-indexers of graphs, to appear. 10.4067/S0716-09172017000200195Suche in Google Scholar

[10] West D. B., Introduction to Graph Theory, Pearson Education, Upper Saddle River, 2001. Suche in Google Scholar

Received: 2016-10-10
Revised: 2016-12-21
Accepted: 2017-1-3
Published Online: 2017-1-20
Published in Print: 2017-4-1

© 2017 by De Gruyter

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