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Edge Co-Even Domination

Year 2025, Volume: 15 Issue: 1, 291 - 297, 01.03.2025

Nazlıcan Çağla Demirpolat , Elgin Kılıç , Ahmed Omran

https://doi.org/10.21597/jist.1460711

Abstract

Domination is one of those important parameters in graph theory which has a very wide range of applications. There are various types of domination depending on the structure of dominating sets. In this study, a new domination parameter called edge co-even domination number is introduced and denoted by γ_coe^' (G). Some basic graphs such as path, cycle, complete, complete bipartite, star, regular, wheel and their complement graphs are examined of this definition. In addition, some results of this parameter are found under graph operations, such as corona and cartesian product.

Keywords

Domination Edge co-even dominating set Edge co-even domination number

References

  • Bondy, J.A., Murty, U.S.R (1976). Graph Theory with Applications. New York.
  • Buckley, F., Harary, F. (1990). Distance in Graphs. Addison-Wesley Publishing Company.
  • Demirpolat, N.Ç., Kılıç, E., (2021). Co-Even Domination Number of Some Path Related Graphs, Journal of Modern Technology and Engineering, Vol. 6, No. 2, pp. 143-150.
  • Erdös, P., Rényi, A. & Sós,V.T., (1996). On a problem of graph theory, Studia Sci. Math. Hungar., 1, 215–235.
  • Hedetniemi, S.T., Haynes, T.W. & Slater, P.J. (1998). Fundamentals of Domination in Graphs. Marcel Dekker Inc.
  • Imran, S. A., & Omran, A. A. (2022, January). Total co-even domination in graphs in some of engineering project theoretically. In AIP Conference Proceedings (Vol. 2386, No. 1). AIP Publishing.
  • Klavžar, S., Imrich, W., Rall, D.F. (2008). Topics in Graph Theory: Graphs and Their Cartesian Product. A K Peters/CRC Press.
  • Mitchell, S., Hedetniemi, S.T. (1977). Edge domination in trees. Congr. Numer., 19, 489-509.
  • Omran, A.A., Shalaan, M. M., (2020). Co-Even Domination in Graphs, International Journal of Control and Automation, Vol. 13, No. 3, pp. 330-334.
  • Omran, A. A., & Shalaan, M. M. (2020, November). Inverse co-even domination of graphs. In IOP Conference Series: Materials Science and Engineering (Vol. 928, No. 4, p. 042025). IOP Publishing.
  • Omran, A.A, & Ibrahim, T. (2021). Fuzzy co-even domination of strong fuzzy graphs. International Journal of Nonlinear Analysis and Applications, 12(1), 726-734.

Year 2025, Volume: 15 Issue: 1, 291 - 297, 01.03.2025

Nazlıcan Çağla Demirpolat , Elgin Kılıç , Ahmed Omran

https://doi.org/10.21597/jist.1460711

Abstract

References

  • Bondy, J.A., Murty, U.S.R (1976). Graph Theory with Applications. New York.
  • Buckley, F., Harary, F. (1990). Distance in Graphs. Addison-Wesley Publishing Company.
  • Demirpolat, N.Ç., Kılıç, E., (2021). Co-Even Domination Number of Some Path Related Graphs, Journal of Modern Technology and Engineering, Vol. 6, No. 2, pp. 143-150.
  • Erdös, P., Rényi, A. & Sós,V.T., (1996). On a problem of graph theory, Studia Sci. Math. Hungar., 1, 215–235.
  • Hedetniemi, S.T., Haynes, T.W. & Slater, P.J. (1998). Fundamentals of Domination in Graphs. Marcel Dekker Inc.
  • Imran, S. A., & Omran, A. A. (2022, January). Total co-even domination in graphs in some of engineering project theoretically. In AIP Conference Proceedings (Vol. 2386, No. 1). AIP Publishing.
  • Klavžar, S., Imrich, W., Rall, D.F. (2008). Topics in Graph Theory: Graphs and Their Cartesian Product. A K Peters/CRC Press.
  • Mitchell, S., Hedetniemi, S.T. (1977). Edge domination in trees. Congr. Numer., 19, 489-509.
  • Omran, A.A., Shalaan, M. M., (2020). Co-Even Domination in Graphs, International Journal of Control and Automation, Vol. 13, No. 3, pp. 330-334.
  • Omran, A. A., & Shalaan, M. M. (2020, November). Inverse co-even domination of graphs. In IOP Conference Series: Materials Science and Engineering (Vol. 928, No. 4, p. 042025). IOP Publishing.
  • Omran, A.A, & Ibrahim, T. (2021). Fuzzy co-even domination of strong fuzzy graphs. International Journal of Nonlinear Analysis and Applications, 12(1), 726-734.
There are 11 citations in total.

Details

Primary Language English
Subjects Pure Mathematics (Other)
Journal Section Matematik / Mathematics
Authors

Nazlıcan Çağla Demirpolat 0000-0002-3137-4422

Elgin Kılıç 0000-0002-1074-5589

Ahmed Omran 0000-0002-8362-530X

Early Pub Date February 20, 2025
Publication Date March 1, 2025
Submission Date May 11, 2024
Acceptance Date November 7, 2024
Published in Issue Year 2025 Volume: 15 Issue: 1

Cite

APA Demirpolat, N. Ç., Kılıç, E., & Omran, A. (2025). Edge Co-Even Domination. Journal of the Institute of Science and Technology, 15(1), 291-297. https://doi.org/10.21597/jist.1460711
AMA Demirpolat NÇ, Kılıç E, Omran A. Edge Co-Even Domination. J. Inst. Sci. and Tech. March 2025;15(1):291-297. doi:10.21597/jist.1460711
Chicago Demirpolat, Nazlıcan Çağla, Elgin Kılıç, and Ahmed Omran. “Edge Co-Even Domination”. Journal of the Institute of Science and Technology 15, no. 1 (March 2025): 291-97. https://doi.org/10.21597/jist.1460711.
EndNote Demirpolat NÇ, Kılıç E, Omran A (March 1, 2025) Edge Co-Even Domination. Journal of the Institute of Science and Technology 15 1 291–297.
IEEE N. Ç. Demirpolat, E. Kılıç, and A. Omran, “Edge Co-Even Domination”, J. Inst. Sci. and Tech., vol. 15, no. 1, pp. 291–297, 2025, doi: 10.21597/jist.1460711.
ISNAD Demirpolat, Nazlıcan Çağla et al. “Edge Co-Even Domination”. Journal of the Institute of Science and Technology 15/1 (March 2025), 291-297. https://doi.org/10.21597/jist.1460711.
JAMA Demirpolat NÇ, Kılıç E, Omran A. Edge Co-Even Domination. J. Inst. Sci. and Tech. 2025;15:291–297.
MLA Demirpolat, Nazlıcan Çağla et al. “Edge Co-Even Domination”. Journal of the Institute of Science and Technology, vol. 15, no. 1, 2025, pp. 291-7, doi:10.21597/jist.1460711.
Vancouver Demirpolat NÇ, Kılıç E, Omran A. Edge Co-Even Domination. J. Inst. Sci. and Tech. 2025;15(1):291-7.
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