International Journal of Nonlinear Analysis and Applications
Fuzzy equality co-neighborhood domination of graphs
Document Type : Research Paper
Authors
1 Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
2 Department of Mathematics, College of Education for Pure Science, University of Babylon, Babylon, Iraq.
3 Department of Applied Sciences, University of Technology Baghdad, Iraq
Abstract
In that paper the fuzzy equality co-neighborhood domination and denoted by $\gamma_{en}(G)$ for a new definition of domination was described for the fuzzy graph. This new definition was studied in a strong fuzzy graph and constraints were found for many several graphs. Complementary strong fuzzy graphs of the same graphs were examined and studied in detail.
Keywords
[1] M. A. Abdlhusein and M. N. Al-Harere, Total pitchfork domination and its inverse in graphs, Dis. Math. Algor.
Appl. (2021) 2150038.
[2] M. A. Abdlhusein and M. N. Al-Harere, New parameter of inverse domination in graphs, Indian J. Pure Appl.
Math. (accepted to appear)(2021).
[3] M. A. Abdlhusein and M. N. Al-Harere, Doubly connected pitchfork domination and its inverse in graphs, TWMS
J. App. Eng. Math. (accepted to appear) (2021).
[4] M. A. Abdlhusein, Stability of inverse pitchfork domination, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 1009–1016.
[5] M. A. Abdlhusein, Doubly connected bi-domination in graphs, Dis. Math. Algor. Appl. 13(2) (2021) 2150009.
[6] M. N. Al-Harere and M. A. Abdlhusein, Pitchfork domination in graphs, Dis. Math. Algor. Appl. 12(2)(2020)
2050025.
[7] M.N. Al-Harere, A. A. Omran, and A. T. Breesam, Captive domination in graphs, Dis. Math. Algor. Appl. 12(6)
(2020) 2050076.
[8] M. N. Al-Harere and P. A. Khuda Bakhash, Tadpole domination in graphs, Baghdad Sci. J. 15 (2018) 466–471.
[9] M. N. Al-Harere, P. A. Khuda, Tadpole domination in duplicated graphs, Dis. Math. Algor. Appl. 13(2) (2021)
2150003.
[10] M. N. Al-Harere, R. J. Mitlf and F. A. Sadiq, Variant domination types for a complete h-ary tree, Baghdad Sci.
J. 18(1) (2021) 2078–8665.
[11] M. N. Al-Harere and A. A. Omran, On binary operation graphs, Bol. Soc. Paranaense Mat. 38(7) (2020) 59–67 .
[12] L. K. Alzaki, M. A. Abdlhusein and A. K. Yousif, Stability of (1,2)-total pitchfork domination, Int. J. Nonlinear
Anal. Appl. 12(2) (2021) 265–274.
[13] C. Berge, The Theory of Graphs and its Applications, Methuen and Co, London, 1962.
[14] A. A. Jabor and A. A. Omran, Hausdorff topological of path in graph, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020)
042008, doi:10.1088/1757-899X/928/4/042008.
[15] S. Sh. Kahat, A. M. Khalaf, R. Hasni, Dominating sets and domination polynomials of stars, Aust. J. Basic Appl.
Sci. 8(6) (2014) 383–386.
[16] S. Sh. Kahat, A. M. Khalaf, Dominating sets and domination polynomial of complete graphs with missing edges,
J. Kufa Math. Comp. 2(1) (2014) 64–68.
[17] S. Sh. Kahat, A. M. Khalaf, R. Hasni, Dominating sets and domination polynomial of wheels, Asian J. Appl. Sci.
2(3) (2014) 287–290.
[18] S. Sh. Kahat, A. M. Khalaf, Dominating Sets and Domination polynomial of kr-gluing of Graphs, J. Dirasat
Tarbawiya, to appear.
[19] S. Sh. Kahat, A. M. Khalaf, Dominating Sets and Domination polynomial of kr-gluing of Graphs II, Dirasat
Tarbawiya, 12(48) (2019) 358–367.
[20] S. Sh. Kahat, M. N. Al-Harere, Inverse Equality Co-Neighborhood Domination in Graphs, journal (IHICPAS). By
”Ibn Al-Haitham 2nd. International Conference for Pure and Applied Science” accepted for publication (2020).
[21] S. Sh. Kahat, M. N. Al-Harere, Total Equality Co-Neighborhood Domination in Graphs, AIP (ISSN: 0094-243X).
ICCEPS-2021. By Sixth National Scientific/ Third International Conference accepted for publication.
[22] S. Sh. Kahat, M. N. Al-Harere, Dominating sets and polynomial of equality co-neighborhood domination of graphs, AIP (ISSN: 0094-243X).ICARPAS. By 1st International Conference on Advanced Research in Pure and Applied Science accepted for publication (2021).
[23] Q. M. Mahioub and N. D. Soner, The split domination number of fuzzy graphs, Far East J. Appl. Math. 30 (2008) 125–132.
[24] A. A. Omran, M. N. Al-Harere, and Sahib Sh. Kahat, Equality co-neighborhood domination in graphs, Disc. Math. Algor. Appl. (2021). https://doi.org/10.1142/S1793830921500981
[25] A. A. Omran and Y. Rajihy, Some properties of frame domination in graphs, J. Eng.Appl. Sci. 12 (2017) 8882–8885.
[26] A. A. Omran and M. M. Shalaan, Inverse co-even domination of graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042025.
[27] A. A. Omran and T. Swadi, Observer domination number in graphs, J. Adv. Res. Dyn. Cont. Syst. 11 (01-Special Issue) (2019) 468–495.
[28] A. A. Omran and H. Hamed Oda, Hn domination in graphs, Baghdad Sci. J. 16(1) (2019) 242–247.
[29] A. A. Omran and M. M. Shalaan, Inverse co-even domination of graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042025. doi:10.1088/1757-899X/928/4/042025.
[30] A. A. Omran and T. A. Ibrahim, Fuzzy co-even domination of strong fuzzy graphs, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 727–734.
Appl. (2021) 2150038.
[2] M. A. Abdlhusein and M. N. Al-Harere, New parameter of inverse domination in graphs, Indian J. Pure Appl.
Math. (accepted to appear)(2021).
[3] M. A. Abdlhusein and M. N. Al-Harere, Doubly connected pitchfork domination and its inverse in graphs, TWMS
J. App. Eng. Math. (accepted to appear) (2021).
[4] M. A. Abdlhusein, Stability of inverse pitchfork domination, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 1009–1016.
[5] M. A. Abdlhusein, Doubly connected bi-domination in graphs, Dis. Math. Algor. Appl. 13(2) (2021) 2150009.
[6] M. N. Al-Harere and M. A. Abdlhusein, Pitchfork domination in graphs, Dis. Math. Algor. Appl. 12(2)(2020)
2050025.
[7] M.N. Al-Harere, A. A. Omran, and A. T. Breesam, Captive domination in graphs, Dis. Math. Algor. Appl. 12(6)
(2020) 2050076.
[8] M. N. Al-Harere and P. A. Khuda Bakhash, Tadpole domination in graphs, Baghdad Sci. J. 15 (2018) 466–471.
[9] M. N. Al-Harere, P. A. Khuda, Tadpole domination in duplicated graphs, Dis. Math. Algor. Appl. 13(2) (2021)
2150003.
[10] M. N. Al-Harere, R. J. Mitlf and F. A. Sadiq, Variant domination types for a complete h-ary tree, Baghdad Sci.
J. 18(1) (2021) 2078–8665.
[11] M. N. Al-Harere and A. A. Omran, On binary operation graphs, Bol. Soc. Paranaense Mat. 38(7) (2020) 59–67 .
[12] L. K. Alzaki, M. A. Abdlhusein and A. K. Yousif, Stability of (1,2)-total pitchfork domination, Int. J. Nonlinear
Anal. Appl. 12(2) (2021) 265–274.
[13] C. Berge, The Theory of Graphs and its Applications, Methuen and Co, London, 1962.
[14] A. A. Jabor and A. A. Omran, Hausdorff topological of path in graph, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020)
042008, doi:10.1088/1757-899X/928/4/042008.
[15] S. Sh. Kahat, A. M. Khalaf, R. Hasni, Dominating sets and domination polynomials of stars, Aust. J. Basic Appl.
Sci. 8(6) (2014) 383–386.
[16] S. Sh. Kahat, A. M. Khalaf, Dominating sets and domination polynomial of complete graphs with missing edges,
J. Kufa Math. Comp. 2(1) (2014) 64–68.
[17] S. Sh. Kahat, A. M. Khalaf, R. Hasni, Dominating sets and domination polynomial of wheels, Asian J. Appl. Sci.
2(3) (2014) 287–290.
[18] S. Sh. Kahat, A. M. Khalaf, Dominating Sets and Domination polynomial of kr-gluing of Graphs, J. Dirasat
Tarbawiya, to appear.
[19] S. Sh. Kahat, A. M. Khalaf, Dominating Sets and Domination polynomial of kr-gluing of Graphs II, Dirasat
Tarbawiya, 12(48) (2019) 358–367.
[20] S. Sh. Kahat, M. N. Al-Harere, Inverse Equality Co-Neighborhood Domination in Graphs, journal (IHICPAS). By
”Ibn Al-Haitham 2nd. International Conference for Pure and Applied Science” accepted for publication (2020).
[21] S. Sh. Kahat, M. N. Al-Harere, Total Equality Co-Neighborhood Domination in Graphs, AIP (ISSN: 0094-243X).
ICCEPS-2021. By Sixth National Scientific/ Third International Conference accepted for publication.
[22] S. Sh. Kahat, M. N. Al-Harere, Dominating sets and polynomial of equality co-neighborhood domination of graphs, AIP (ISSN: 0094-243X).ICARPAS. By 1st International Conference on Advanced Research in Pure and Applied Science accepted for publication (2021).
[23] Q. M. Mahioub and N. D. Soner, The split domination number of fuzzy graphs, Far East J. Appl. Math. 30 (2008) 125–132.
[24] A. A. Omran, M. N. Al-Harere, and Sahib Sh. Kahat, Equality co-neighborhood domination in graphs, Disc. Math. Algor. Appl. (2021). https://doi.org/10.1142/S1793830921500981
[25] A. A. Omran and Y. Rajihy, Some properties of frame domination in graphs, J. Eng.Appl. Sci. 12 (2017) 8882–8885.
[26] A. A. Omran and M. M. Shalaan, Inverse co-even domination of graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042025.
[27] A. A. Omran and T. Swadi, Observer domination number in graphs, J. Adv. Res. Dyn. Cont. Syst. 11 (01-Special Issue) (2019) 468–495.
[28] A. A. Omran and H. Hamed Oda, Hn domination in graphs, Baghdad Sci. J. 16(1) (2019) 242–247.
[29] A. A. Omran and M. M. Shalaan, Inverse co-even domination of graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042025. doi:10.1088/1757-899X/928/4/042025.
[30] A. A. Omran and T. A. Ibrahim, Fuzzy co-even domination of strong fuzzy graphs, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 727–734.
[31] S. J. Radhi, M. A. Abdlhusein and A. E. Hashoosh, The arrow domination in graphs, Int. J. Nonlinear Anal. Appl. 12(1) (2021) 473–480.
[32] M. M. Shalaan and A. A. Omran, Co-even domination number in some graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042015. doi:10.1088/1757-899X/928/4/042015.
[33] A. Somasundaram and S. Somasundaram, 1975, Domination in fuzzy graphs-I, Pattern Rec. Lett.19 (1998) 787–791.
[34] A. Somasundaram, Domination in fuzzy graphs-II, J. Fuzzy Math. 13 (2005) 281–288.
[35] S. H. Talib, A. A. Omran , and Y. Rajihy, Additional properties of frame domination in graphs, J. Phys.: Conf. Ser. 1664 (2020) 012026, doi:10.1088/1742-6596/1664/1/012026.
[36] S. H. Talib, A. A. Omran , and Y. Rajihy , Inverse frame domination in graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042024, doi:10.1088/1757-899X/928/4/042024.
[37] D. A. Xavior, F. Isido and V. M. Chitra, On domination in fuzzy graphs, Int. J. Comput. Algor. 2 (2013) 248–250.
[38] H. J. Yousif and A. A. Omran, The Split Anti Fuzzy Domination in Anti Fuzzy Graphs, J. Phys., Conf. Ser. 1591 (2020) 012054. doi:10.1088/1742-6596/1591/1/012054.
[39] H. J. Yousif and A. A. Omran, 2-anti fuzzy domination in anti fuzzy graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042027.
[32] M. M. Shalaan and A. A. Omran, Co-even domination number in some graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042015. doi:10.1088/1757-899X/928/4/042015.
[33] A. Somasundaram and S. Somasundaram, 1975, Domination in fuzzy graphs-I, Pattern Rec. Lett.19 (1998) 787–791.
[34] A. Somasundaram, Domination in fuzzy graphs-II, J. Fuzzy Math. 13 (2005) 281–288.
[35] S. H. Talib, A. A. Omran , and Y. Rajihy, Additional properties of frame domination in graphs, J. Phys.: Conf. Ser. 1664 (2020) 012026, doi:10.1088/1742-6596/1664/1/012026.
[36] S. H. Talib, A. A. Omran , and Y. Rajihy , Inverse frame domination in graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042024, doi:10.1088/1757-899X/928/4/042024.
[37] D. A. Xavior, F. Isido and V. M. Chitra, On domination in fuzzy graphs, Int. J. Comput. Algor. 2 (2013) 248–250.
[38] H. J. Yousif and A. A. Omran, The Split Anti Fuzzy Domination in Anti Fuzzy Graphs, J. Phys., Conf. Ser. 1591 (2020) 012054. doi:10.1088/1742-6596/1591/1/012054.
[39] H. J. Yousif and A. A. Omran, 2-anti fuzzy domination in anti fuzzy graphs, IOP Conf. Ser.: Mater. Sci. Eng. 928 (2020) 042027.
)
Volume 12, Issue 2
November 2021Pages 537-545
- Receive Date: 27 October 2020
- Revise Date: 12 May 2021
- Accept Date: 16 June 2021