Split Legendary Domination in graphs

Authors

DOI:

https://doi.org/10.23755/rm.v51i0.1235

Keywords:

Split domination number, legendary domination number, split legendary domination number.

Abstract

Harary and Norman introduced the line graph L(G) . We introduced the legendary domination number by combining the domination concept both in graph and its line graph. In this paper, the split domination property is studied along with the legendary domination concept. Hence the split legendary dominating set is introduced and the corresponding split legendary domination number is defined for the line graph L(G). Also, the graph theoretical parameters are studied in terms of elements of G and its relationship with other domination parameters are presented.

References

Harary, F. (1969). Graph theory. Addison Wesley, Reading, MA.

Harary, F., & Norman, R. (1960). Some properties of line graphs. Rendiconti del Circolo Matematico di Palermo, 9(2), 161-169.

Jayaram, S. R. (1987). Line domination in graphs. Graphs and Combinatorics, 3(1), 357-363.

Haynes, T. W., Hedetniemi, S. T., & Slater, P. J. (1998). Fundamentals of Domination in Graphs. Marcel Dekker, Inc, New York.

Kulli, V. R. (2010). Theory of Domination in Graphs. Vishwa International Publication, Gulbarga, India.

Kulli, V. R., & Janakiram, B. (1997). The Split domination number of a graph. Graph Theory Notes of New York, XXXII, 16-19.

Mohanaselvi, V., & Kavitha, P. (2016). The Legendary domination in Graphs. International Journal of Scientific and Engineering Research, 7(5), ISSN 2228-5518.

Mohanaselvi, V., & Kavitha, P. (2016). The Legendary Complement Domination in Graphs. Bulletin of Pure and Applied Mathematics, 1(1), 14-25.

Mohanaselvi, V., Kavitha, P., & Durka Devi, M. (2016). The Split Complement Line Domination in Graphs. International Research Journal of Mathematics, Engineering and IT, 3(10), 47-62.

Mohanaselvi, V., Kavitha, P., & Durka Devi, M. (2017). The Non Split Complement Line Domination in Graphs. Journal of Informatics and Mathematical Sciences, 9(3), 1-14.

Mohanaselvi, V., & Kavitha, P. (2018). Legendary Line Domination in L(L(G)). International Journal of Research in Avent Technology, 6(8), 2118-2124.

Mohanaselvi, V., & Kavitha, P. (2017). Domination of line neighbourhood graphs. International Journal of Pure and Applied Mathematics, 113(10), 343-351.

Muddebihal, M. H., Panfarosh, U. A., & Seetamkar, A. R. (2012). Split line domination in graphs. International Journal of Science and Research, 1163-1166.

Ore, O. (1962). Theory of graphs. American Mathematical Society. Colloquium Publications, 38, Providence.

Gupta, P., Singh, R., & Arumugam, S. (2020). Graphs with equal domination and independent domination number. AKCE International Journal of Graphs and Combinatorics, 17(2), 691-696.

Gupta, P., Goyal, A., & Jain, R. (2021). Independent point-set domination in line graphs. AKCE International Journal of Graphs and Combinatorics, 18(3), 180-185.

Aeja, S., Raghav, J. S., & Akka, D. G. (2022). Set-Domination in line graphs. Journal of Emerging Technologies and Innovative Research, 9(7), H108-H115.

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Published

2024-03-02

Issue

Vol. 51 (2024)

Section

Volume 51-2024

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