Keywords and phrases: k-domination defect, minimum dominating set, composition of graphs.
Received: April 28, 2023; Revised: May 20, 2023: Accepted: June 8, 2023; Published: June 30, 2023
How to cite this article: Aldwin T. Miranda and Rolito G. Eballe, Domination defect in the composition of graphs, Advances and Applications in Discrete Mathematics 39(2) (2023), 209-219. http://dx.doi.org/10.17654/0974165823048
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] A. Das and W. J. Desormeaux, Domination defect in graphs: guarding with fewer guards, Indian J. Pure Appl. Math. 49(2) (2018), 349-364. [2] A. T. Miranda and R. G. Eballe, Domination defect for the join and corona of graphs, Applied Mathematical Sciences 15(12) (2021), 615-623. DOI: 10.12988/ams.2021.914597 [3] A. T. Miranda and R. G. Eballe, Domination defect in the edge corona of graphs, Asian Research Journal of Mathematics 18(2) (2022), 95-101. DOI: 10.9734/ARJOM/2022/v18i12628 [4] A. T. Miranda and R. G. Eballe, Domination defect of some parameterized families of graphs, Communications in Mathematics and Applications (accepted for publication on Dec. 17, 2022). [5] M. P. Militante and R. G. Eballe, Weakly connected 2-domination in the lexicographic product of graphs, International Journal of Mathematical Analysis 16(3) (2022), 125-132. DOI: 10.12988/ijma.2022.912428 [6] B. L. Susada and R. G. Eballe, Independent semitotal domination in the join of graphs, Asian Research Journal of Mathematics 19(3) (2023), 25-31. DOI: 10.9734/ARJOM/2023/v19i3647 [7] G. J. Madriaga and R. G. Eballe, Clique Centrality and Global Clique Centrality of Graphs, Asian Research Journal of Mathematics 19(2) (2023), 9-16. DOI: 10.9734/ARJOM/2023/v19i2640 [8] C. B. Balandra and S. R. Canoy, Jr., Another look at p-liar’s domination in graphs, International Journal of Mathematical Analysis 10(5) (2016), 213-221. http://dx.doi.org/10.12988/ijma.2016.511283 [9] R. G. Eballe, R. Aldema, E. M. Paluga, R. F. Rulete and F. P. Jamil, Global defensive alliances in the join, corona and composition of graphs, Ars Comb. 107 (2012), 225-245. [10] M. P. Militante and R. G. Eballe, Restrained weakly connected 2-domination in the join of graphs, Communications in Mathematics and Applications 13(3) (2022), 1087-1096. DOI: 10.26713/cma.v13i3.1939 [11] L. Chartrand, P. Lesniak and Zhang, Graphs and Digraphs (Discrete Mathematics and its Applications) (6th ed.), Chapman and Hall/CRC, 2015. [12] R. G. Eballe and S. R. Canoy, Jr., The essential cutset number and connectivity of the join and composition of graphs, Utilitas Mathematica 84(1) (2011), 257-264. [13] C. L. Armada, S. R. Canoy and C. E. Go, Forcing domination numbers of graphs under some binary operations, Advances and Applications in Discrete Mathematics 19(3) (2018), 213-228. http://dx.doi.org/10.17654/DM019030213 [14] E. J. Cockayne, R. M. Dawes and S. T. Hedetniemi, Total domination in graphs, Networks 10(3) (1980), 211-219. https://doi.org/10.1002/net.3230100304
|