On Pitchfork Domination Number of Corona of Some Graphs
DOI:
https://doi.org/10.26713/cma.v15i5.2866Keywords:
Domination, Pitchfork domination, Corona, JoinAbstract
A dominating set \(D\) of \(V\) is called a pitchfork dominating set if every vertex in it dominates at least \(j\) vertices and at most \(k\) vertices of \(V-D\), for any non-negative integers \(j\) and \(k\). The pitchfork domination number of \(G\), denoted by \(\gamma_{pf} (G)\) is the minimum cardinality over all pitchfork dominating sets in \(G\). In this paper, the pitchfork domination when \(j=1\) and \(k=2\) are applied to the corona of some graphs: \(G \circ C_m\), \(G \circ K_{1,n}\), \(G \circ K_{p,q}\), \(G \circ B_{2,k}\) and \(G \circ F_{2,k}\). In relation to getting new results of the corona of the mentioned graphs, we also generate results of pitchfork domination number of \(P_2+\overline{K}_n\), \(K_1 + K_{p,q}\), \(B_{2,k}\), \(F_{2,k}\) and \(K_1 + F_{2,k}\).
Downloads
References
M. A. Abdlhusein and M. N. Al-Harere, Pitchfork domination and its inverse for corona and join operations in graphs, Proceedings of International Mathematical Sciences 1(2) (2019), 51 – 55.
M. N. Al-Harere and M. A. Abdlhusein, Pitchfork domination in graphs, Discrete Mathematics, Algorithms and Applications 12(02) (2020), 2050025, DOI: 10.1142/S1793830920500251.
A. Aslam, J. L. G. Guirao, S. Ahmad and W. Gao, Topological indices of the line graph of subdivision graph of complete bipartite graphs, Applied Mathematics & Information Sciences 11 (2017), 1631 – 1636, DOI: 10.18576/amis/110610.
Asmiati, Locating chromatic number of banana tree, International Mathematical Forum 12(1) (2017), 39 – 45, DOI: 10.12988/imf.2017.610138.
G. Chartrand and P. Zhang, Chromatic Graph Theory, 1st edition, Chapman and Hall/CRC, New York, 504 pages (2008), DOI: 10.1201/9781584888017.
A. Gayathri, A. Muneera, T. N. Rao and T. S. Rao, Study of various dominations in graph theory and its applications, International Journal of Scientific & Technology Research 9(2) (2020), 3426 – 3429.
A. Haryanti, D. Indriati and T. S. Martini, On the total vertex irregularity strength of firecracker graph, Journal of Physics: Conference Series 1211 (2019), 012011, DOI: 10.1088/1742-6596/1211/1/012011.
T. W. Haynes, S. T. Hedetneime and P. J. Slater, Domination in Graphs, Volume 2: Advanced Topics, 1st Edition, Routledge, 520 pages (1998), DOI: 10.1201/9781315141428.
R. Venkateswari, Applications of domination graphs in real life, Journal of Composition Theory 12 (2019), 22 – 28.
Downloads
Published
How to Cite
Issue
Section
License
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.
