Edge Co-Even Domination

Öz

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.

Anahtar Kelimeler

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

Kaynakça

1. Bondy, J.A., Murty, U.S.R (1976). Graph Theory with Applications. New York.
2. Buckley, F., Harary, F. (1990). Distance in Graphs. Addison-Wesley Publishing Company.
3. 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.
4. Erdös, P., Rényi, A. & Sós,V.T., (1996). On a problem of graph theory, Studia Sci. Math. Hungar., 1, 215–235.
5. Hedetniemi, S.T., Haynes, T.W. & Slater, P.J. (1998). Fundamentals of Domination in Graphs. Marcel Dekker Inc.
6. 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.
7. Klavžar, S., Imrich, W., Rall, D.F. (2008). Topics in Graph Theory: Graphs and Their Cartesian Product. A K Peters/CRC Press.
8. Mitchell, S., Hedetniemi, S.T. (1977). Edge domination in trees. Congr. Numer., 19, 489-509.

9. 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.
10. 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.
11. 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.