Forcing Clique Domination in Graphs

Authors

  • Cris L. Armada Faculty of Applied Science, Vietnam National University - Ho Chi Minh City University of Technology Ho Chi Minh City, Vietnam
  • Edward M. Kiunisala Mathematics Department, College of Computing, Artificial Intelligence and Sciences, Cebu Normal University, 6000 Cebu City, Philippines
  • Cristopher John S. Rosero Mathematics Department, College of Computing, Artificial Intelligence and Sciences, Cebu Normal University, 6000 Cebu City, Philippines
  • Jeneveb T. Malusay Mathematics Department, College of Computing, Artificial Intelligence and Sciences, Cebu Normal University, 6000 Cebu City, Philippines

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6065

Keywords:

forcing, clique domination, join, corona, lexicographic product

Abstract

The clique domination number of some special graphs such as paths, cycles, complete graphs, generalized wheels, generalized fans, and complete bipartite graphs is presented. The forcing clique domination number of these graphs, along with binary operations such as join, corona, and lexicographic product of two graphs, is also determined. Connected graphs with forcing clique domination number equal to $0$, $1$, or $a$, where $a$ is greater than $1$ but less than the clique domination number, are characterized. Necessary and sufficient conditions for the forcing clique domination number to be equal to the clique domination number are given. Since some of the graphs in this study do not have a clique dominating set, the forcing clique domination number is undefined in those cases.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Discrete Mathematics

License

Copyright (c) 2025 Cris L. Armada, Edward M. Kiunisala, Cristopher John S. Rosero, Jeneveb T. Malusay

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How to Cite

Forcing Clique Domination in Graphs. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6065. https://doi.org/10.29020/nybg.ejpam.v18i2.6065