The Investigating Weakly Connected 2-Domination in the Complementary Prism of Graphs and in Some Unary Graph Operations

Authors

  • Mae Militante Mindanao State University General Santos
  • Doli-jane Mindanao State University - General Santos
  • Nadjua
  • Francis Mindanao State University - General Santos
  • Emmanuel Mindanao State University - General Santos

Keywords:

weakly connected 2-domination, complementary prism, edge deletion, vertex deletion, unary operations, line graphs

Abstract

This paper dealt with the concepts of weakly connected 2- domination in the complementary prisms of graphs and graphs obtained by reducing their edges and vertices. In particular, bounds and exact values of the weakly connected 2- domination number in the complementary prism of graphs, graphs resulting from deleting an edge and vertex and line graphs are presented. In addition, properties of the graphs with weakly connected 2- domination number of complementary prism equal to 2 and 3, are provided.

Downloads

Download data is not yet available.

References

A. Alhashim, W. J. Desormeaux and T. W. Haynes, Roman Domination in Complementary

Prisms, Australian Journal of Combinatorics, 68(2), 218– 228 (2017).

G. Chartrand, L. Lesniak and P. Zhang, Graphs and Digraphs, 6th edition, CRC Press,

New York (2016), doi:10.1201/b19731.

J. E. Dunbar, J. W.Grossman, J. H. Hattingh, S.T. Hedetniemi and A. A. McRae,

On Weakly Connected Domination in Graphs, Discrete Mathematics 261– 269

(1997),doi:10.1016/S0012 365X(96)00233-6

J. F. Fink and M. S. Jacobson, On n-Domination, n-Dependence and Forbidden Subgraphs,

Graph Theory with Applications to Algorithms and Computer Science, Wiley, New York

(1985), 301– 312.

M. Lemanska, Domination Numbers in Graphs with Removed Edge or Set of Edges, Dis

cussiones Mathematicae, 25, 51–56 (2005).

M. P. Militante and R.G. Eballe. Weakly Connected 2-Domination in Some Special Graphs.

Applied Mathematical Sciences, 15(12), 579– 586 (2021). doi:10.12988/ams.2021.914590.

M. P. Militante and R.G. Eballe. Exploring the Vertex and Edge Corona of Graphs for

their Weakly Connected 2-Domination. International Journal of Contemporary Mathematical Sciences, 16(4), 161– 172 (2021). doi:10.12988/ijcms.2021.91633 .

M. P. Militante, R.G. Eballe, and R. E. Leonida. Restrained Weakly Connected 2

Domination in the Join of Graphs. Communications in Mathematics and Applications,

(3), 1087– 1096 (2022). doi:10.26713/cma.v13i3.1939.

S. Ot’avio and M. R. Cappelle. k-Independence on Complementary Prism Graphs.

Matem´atica Contempor’anea, 48, 211– 220 (2021).doi:10.21711/231766362021/rmc4821.

Published

13-08-2025

How to Cite

Militante, M., Tejada, D.- jane, Seddic, N., Demata, F. N., & Campos, E. (2025). The Investigating Weakly Connected 2-Domination in the Complementary Prism of Graphs and in Some Unary Graph Operations. Communications in Mathematics and Applications, 16(1). Retrieved from https://www.journals.rgnpublications.com/index.php/cma/article/view/2837

Issue

Vol. 16 No. 1 (2025)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.