Superior domination polynomial of cycles

R Tejaskumar

Abstract


Superior domination polynomial SD(G, x) is a polynomial in which the power of the variable denotes the cardinality of a superior dominating set and the total number of sets of same cardinality forms the coefficient of the variable. In this paper we find the SD(Cn, x) of cycle graphs. The results related to the polynomial SD(Cn, x) is stated and the proved.


Keywords


Superior distance, superior domination, neighbourhood vertex, superior domination polynomial.

Full Text:

PDF

References


S. Alikhani and Y. Hock Peng, "Introduction to domination polynomial of a graph," arXiv preprint arXiv:0905.2251, 2009.

F. Harary, "Graph theory," Narosa Publ. House, New Delhi, 2001.

T. Haynes, "Domination in graphs: volume 2: advanced topics," Routledge, 2017.

A.M. Ismayil and R. Tejaskumar, "Eccentric domination polynomial of graphs," Advances in Mathematics: Scientific Journal, vol. 9, pp. 1729-1739, 2020.

T. Janakiraman, M. Bhanumathi, and S. Muthammai, "Eccentric domination in graphs," International Journal of Engineering Science, Advanced Computing and Bio-Technology, vol. 1, no. 2, pp. 1-16, 2010.

K. Kathiresan and G. Marimuthu, "Superior domination in graphs," Utilitas Mathematica, vol. 76, p. 173, 2008.

K. Kathiresan, G. Marimuthu, and S. West, "Superior distance in graphs," Journal of combinatorial mathematics and combinatorial computing, vol. 61, p. 73, 2007.

O. Ore, "Path problems," Theory of graphs, 1962.




DOI: http://dx.doi.org/10.23755/rm.v47i0.819

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Tejaskumar R

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.