Reserved Domination Number of Line Graph
DOI:
https://doi.org/10.12723/mjs.sp1.5Keywords:
Dominating set, reserved dominating set, reserved domination number, line graphAbstract
The reserved dominating set is special up gradation of domination set; where in some of the vertices in the vertex set have special privilege (reserved) to appear in the Dominating set irrespective of their adjacency due to the necessity of the user. The minimum cardinality of a reserved dominating set of G is called the reserved domination number of G and is denoted by R(k) -Y(G) where k is the number of reserved vertices. In this paper reserved domination number of (LPn), (LCn), L(Sn), L(Bm,n), L(Wn) and L(F l,n ) have been found.
References
O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ., Vol.38, Providence, 1962.
J. T. Gross and J. Yellen, Graph Theory and Its Applications, 2nd ed., Boca Raton, FL: CRC Press, pp. 20 and 265, 2006.
G. Rajasekar and G. Rajasekar, “Reserved Domination Number of Graphs,” Turkish Online Journal of Qualitative Inquiry (TOJQI), vol. 12, issue 6, pp. 9199-9209, 2021.
G. Rajasekar and K. Nagarajan, “Location Domination Number of Line Graph,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 22, no. 5, pp. 777-786, 2019.
Dr. G. Rajasekar and G. Rajasekar, “Reserved Domination Numberof some Graphs,” Turkish Journal of Computer and Mathematics Education, vol. 12, no. 11, pp. 2166-2181, 2021.
G. Rajasekar and Govindan Rajasekar, “2-Reserved Domination Number of Graphs,” Advances and Applications in Discrete Mathematics, vol. 27, no. 2, pp. 249-264, 2021.
Additional Files
Published
Issue
Section
License
Copyright (c) 2023 Rajasekar G, G. Rajasekar
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
