DOI: https://doi.org/10.14710/jfma.v6i1.16608

A CLOSER LOOK AT A PATH DOMINATION NUMBER IN GRID GRAPHS

*Leomarich F Casinillo orcid scopus  -  Department of Mathematics, Visayas State University, Philippines

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Abstract

This article exposes the combinatorial formula that determines the path
domination number in a grid graph and discusses some of its properties. Seven properties
are derived regarding the path domination number of grid graphs. Furthermore, some additional
properties as direct consequences of the derived main properties are also
discussed.

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Keywords: Grid graph, path domination number, combinatorial formula

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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  1. Cockayne, E. J., & Hedetniemi, S. T. (1977). Towards a theory of domination in graph. Networks Advanced Topics, 7, 247–261
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  4. Quadras, J., Mahizl, A. S. M., Rajasingh, I., & Rajan, R. S. (2015). Domination in certain chemical graphs. Journal of Mathematical Chemistry, 53(1), 207-219
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  6. Borzooei, R. A., & Rashmanlou, H. (2015). Domination in vague graphs and its applications. Journal of Intelligent & Fuzzy Systems, 29(5), 1933-1940
  7. Rashmanlou, H., Lakdashti, A., & Sabet, S. S. (2018). A Study on Domination Sets in Vague Graphs with Novel Applications. Annals of Pure and Applied Mathematics, 16(1), 223-234
  8. Casinillo, E. L., Casinillo, L. F., Valenzona, J. S., & Valenzona, D. L. (2020). On Triangular Secure Domination Number. InPrime: Indonesian Journal of Pure and Applied Mathematics, 2(2), 105-110
  9. Alcón, L. G. (2016). A note on path domination. Discussiones Mathematicae Graph Theory, 36, 1021–1034
  10. Mekala, A., Kumar, U. V. C., & Murali, R. (2020). Domination and s-path domination in some brick product graphs. Malaya Journal of Matematik (MJM), 8(1, 2020), 254-257
  11. Casinillo, L. F. (2020). Odd and even repetition sequences of independent domination number. Notes on Number Theory and Discrete Mathematics, 26(1), 8-20
  12. Gross, J. L., & Yellen, J. (2003). Handbook of graph theory. CRC press
  13. Hadlock, F. O. (1977). A shortest path algorithm for grid graphs. Networks, 7(4), 323-334
  14. Itai, A., Papadimitriou, C. H., & Szwarcfiter, J. L. (1982). Hamilton paths in grid graphs. SIAM Journal on Computing, 11(4), 676-686
  15. Chartrand, G., & Zhang, P. (2012). A First Course in Graph Theory. Dover Publication Inc., New York
  16. Casinillo, E. L., & Casinillo, L. F. (2020). A Note on Full and Complete Binary Planar Graphs. Indonesian Journal of Mathematics Education, 3(2), 70-75
  17. Casinillo, L. F. (2018). A note on Fibonacci and Lucas number of domination in path. Electronic Journal of Graph Theory and Applications (EJGTA), 6(2), 317-325
  18. Casinillo, L. F. (2020). New counting formula for dominating sets in path and cycle graphs. Journal of Fundamental Mathematics and Applications (JFMA), 3(2), 170-177

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