International Journal of Nonlinear Analysis and Applications
Rings domination in graphs
Document Type : Research Paper
Authors
Department of Applied Sciences, University of Technology, Iraq
Abstract
The aim of this paper is to introduce a new parameter of domination in graphs called "Rings Domination Number". Some properties and important boundaries of the rings dominating set and rings domination number have been discussed. Also, this number for certain graphs have been determined. Furthermore, some operations on two graphs as join, composition, cross product and corona, have been introduced and determined the rings domination numbers for each one of them.
Keywords
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Anal. Appl. 12 (2021), no. 2, 265–274.
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(2022), no. 3, 032036.
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[21] S.S. Majeed, A.A.A. Omran and M.N. Yaqoob, Modern Roman domination of corona of cycle graph with some
certain graphs, Int. J. Math. Comput. Sci. 17 (2022), no. 1, 317–324.
[22] A.A. Omran, Domination and independence in cubic chessboard, Eng. Tech. J. 34 (2016), no. 1 Part (B) Scientific,
59–64.
[23] A.A. Omran, Domination and independence on square chessboard, Eng. Tech. J. 35 (2017), no. 1 Part B, 68–75.
[24] A.A. Omran, M.N. Al-Harere and S.S. Kahat, Equality co-neighborhood domination in graphs, Discrete Math
Algor. Appl. 14 (2022), no. 1, 2150098.[25] A.A. Omran and T.A. Ibrahim, Fuzzy co-even domination of strong fuzzy graphs, Int. J. Nonlinear Anal. Appl.
12 (2021), no. 1, 727–734.
[26] O. Ore, Theory of graphs, American Mathematical Soc. 1962.
[27] S. Salah, A.A. Omran and M.N. Al-Harere, Modern Roman domination on two operations in certain graphs, AIP
Conf. Proc. 2386 (2022), no. 1, 060014.
[28] S. Salah, A.A. Omran and M.N. Al-Harere, Modern Roman domination in fan graph and double fun graph, Eng.
Tech. J. 2022 (2022).
[29] S.H. Talib, A.A. Omran and Y. Rajihy, Inverse frame domination in graphs, 2020 IOP Conf. Ser.: Mater. Sci.
Eng. 928 (2020), 042024.
[30] H.J. Yousif and A.A. Omran, Inverse 2-anti fuzzy domination in anti fuzzy graphs, J. Phys.: Conf. Ser. 1818
(2021), no. 1, 012072.
[31] H.J. Yousif and A.A. Omran, Some results on the n-fuzzy domination in fuzzy graphs, J. Phys.: Conf. Ser. 1879
(2021), no. 3, 032009.
[32] H.J. Yousif and A.A. Omran, Closed fuzzy dominating set in fuzzy graphs, J. Phys.: Conf. Ser. 1879 (2021), no.
3, 032022.
Sci. 14 (2019), no. Special Issue 8, 10375–10379.
[2] M.A. Abdlhusein and M.N. Al-Harere, Total pitchfork domination and its inverse in graphs, Discrete Math. Algor.
Appl. 13 (2021), no. 4, 2150038.
[3] Z.H. Abdulhasan and M.A. Abdlhusein, An inverse triple effect domination in graphs, Int. J. Nonlinear Anal.
Appl. 12 (2021), no. 2, 913–919.
[4] Z.H. Abdulhasan and M.A. Abdlhusein, Triple effect domination in graphs, AIP Conf. Proc. 2386 (2022), no. 1,
060013.
[5] K.S. Al’Dzhabri, A.A. Omran and M.N. Al-Harere, DG-domination topology in digraph, J. Prime Res. Math. 17
(2021), no. 2, 93–100.
[6] M.N. Al-Harere and M.A. Abdlhusein, Pitchfork domination in graphs, Discrete Math. Algor. Appl. 12 (2020),
no. 2, p. 2050025.
[7] M.N. Al-Harere and M.A. Abdlhusein, Some modified types of pitchfork domination and its inverse, Bol. Soc.
Paranaense Mat. 40 (2022), 1–9.
[8] M.N. Al-Harere and A.T. Breesam, Further results on bi-domination in graphs, AIP Conf. Proc. 2096 (2019),
no. 1, 020013.
[9] M.N. Al-Harere and P.A. Khuda Bakhash, Tadpole domination in duplicated graphs, Discrete Math. Algor. Appl.
13 (2021), no. 2, 2150003.
[10] M.N. Al-Harere, R.J. Mitlif and F.A. Sadiq, Variant domination types for a complete h-ary tree, Baghdad Sci. J.
18 (2021), no. 1.
[11] L.K. Alzaki, M.A. Abdlhusein and A.K. Yousif, Stability of (1,2)-total pitchfork domination, Int. J. Nonlinear
Anal. Appl. 12 (2021), no. 2, 265–274.
[12] M.N. Al-Harere, A.A. Omran and A.T. Breesam, Captive domination in graphs, Discrete Math. Algor. Appl. 12
(2020), no. 6, 2050076.
[13] C. Berge, The theory of graphs and its applications, Methuen, 1962.
[14] F. Harary, Graph Theory, Addison-Wesley Publishing Company, 1969.
[15] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of domination in graphs, CRC Press, 1998.
[16] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: volume 2: advanced topics, Taylor &
Francis, 1998.
[17] T.A. Ibrahim and A.A. Omran, Restrained whole domination in graphs, J. Phys.: Conf. Ser. 1879 (2021), no. 3,
032029.
[18] A.A. Jabor and A.A. Omran, Topological domination in graph theory, AIP Conference Proc. 2334 (2021), 020010.
[19] S.S. Kahat and M.N. Al-Harere, Inverse equality co-neighborhood domination in graphs, J. Phys.: Conf. Ser. 1879
(2022), no. 3, 032036.
[20] S.S. Kahat, A.A. Omran and M.N. Al-Harere, Fuzzy equality co-neighborhood domination of graphs, Int. J. Nonlinear Anal. Appl. 12 (2021), no. 2, 537–545.
[21] S.S. Majeed, A.A.A. Omran and M.N. Yaqoob, Modern Roman domination of corona of cycle graph with some
certain graphs, Int. J. Math. Comput. Sci. 17 (2022), no. 1, 317–324.
[22] A.A. Omran, Domination and independence in cubic chessboard, Eng. Tech. J. 34 (2016), no. 1 Part (B) Scientific,
59–64.
[23] A.A. Omran, Domination and independence on square chessboard, Eng. Tech. J. 35 (2017), no. 1 Part B, 68–75.
[24] A.A. Omran, M.N. Al-Harere and S.S. Kahat, Equality co-neighborhood domination in graphs, Discrete Math
Algor. Appl. 14 (2022), no. 1, 2150098.[25] A.A. Omran and T.A. Ibrahim, Fuzzy co-even domination of strong fuzzy graphs, Int. J. Nonlinear Anal. Appl.
12 (2021), no. 1, 727–734.
[26] O. Ore, Theory of graphs, American Mathematical Soc. 1962.
[27] S. Salah, A.A. Omran and M.N. Al-Harere, Modern Roman domination on two operations in certain graphs, AIP
Conf. Proc. 2386 (2022), no. 1, 060014.
[28] S. Salah, A.A. Omran and M.N. Al-Harere, Modern Roman domination in fan graph and double fun graph, Eng.
Tech. J. 2022 (2022).
[29] S.H. Talib, A.A. Omran and Y. Rajihy, Inverse frame domination in graphs, 2020 IOP Conf. Ser.: Mater. Sci.
Eng. 928 (2020), 042024.
[30] H.J. Yousif and A.A. Omran, Inverse 2-anti fuzzy domination in anti fuzzy graphs, J. Phys.: Conf. Ser. 1818
(2021), no. 1, 012072.
[31] H.J. Yousif and A.A. Omran, Some results on the n-fuzzy domination in fuzzy graphs, J. Phys.: Conf. Ser. 1879
(2021), no. 3, 032009.
[32] H.J. Yousif and A.A. Omran, Closed fuzzy dominating set in fuzzy graphs, J. Phys.: Conf. Ser. 1879 (2021), no.
3, 032022.
)
Volume 13, Issue 2
July 2022Pages 1833-1839
- Receive Date: 14 February 2022
- Revise Date: 26 March 2022
- Accept Date: 22 April 2022