Fair Secure Dominating Set in the Corona of Graphs

  • Lorelyn P. Gomez
  • Enrico L. Enriquez
Keywords: Fair Dominating Set, Secure Dominating Set, Fair Secure Dominating Set, Corona, Cartesian Product

Abstract

In this paper, we extend the concept of fair secure dominating sets by characterizing the corona of two nontrivial connected graphs and give some important results.

Downloads

Download data is not yet available.

References

G. Chartrand & P. Zhang. (2012). A first course in graph theory. New York: Dover Publication, Inc.

O. Ore. (1962). Theory of graphs. American Mathematical Society Colloquium Publications, 38. (American Mathematical Society, Providence, RI).

D.P. Salve & E.L. Enriquez. (2016). Inverse perfect domination in the composition and cartesian product of graphs. Global Journal of Pure and Applied Mathematics, 2(1), 1-10.

C. M. Loquias, E. L. Enriquez, & J. Dayap. (2017). Inverse clique domination in graphs. Recoletos Multidisciplinary Research Journal, 4(2), 23-34.

E.L. Enriquez & S.R. Canoy, Jr. (2015). On a variant of convex domination in a graph. International Journal of Mathematical Analysis, 9(32), 1585-1592.

J.A. Dayap & Enriquez. (2020). Outer-convex domination in graphs. Discrete Mathematics, Algorithms and Applications, 12(01), 2050008. Available at: https://doi.org/10.1142/S1793830920500081.

E.L. Enriquez & S.R. Canoy, Jr. (2015). Restrained convex dominating sets in the corona and the products of graphs. Applied Mathematical Sciences, 9(78), 3867-3873.

T.J. Punzalan & E.L. Enriquez. (2016). Inverse restrained domination in graphs. Global Journal of Pure and Applied Mathematics, 3, 1-6.

R.C. Alota & E.L. Enriquez. (2016). On disjoint restrained domination in graphs. Global Journal of Pure and Applied Mathematics, 12(3), 2385-2394.

E.L. Enriquez. (2018). Super restrained domination in the corona of graphs. International Journal of Latest Engineering Research and Applications, 3(5), 1-6.

J.A. Dayap & E.L. Enriquez. (2019). Outer-convex domination in the composition and cartesian product of graphs. Journal of Global Research in Mathematical Archives, 6(3), 34-42.

G.M. Estrada, C.M. Loquias, E.L. Enriquez, & C.S. Baraca. (2019). Perfect doubly connected domination in the join and corona of graphs. International Journal of Latest Engineering Research and Applications, 4(7), 17-21.

Caro, Y., Hansberg, A., & Henning, M. (2011). Fair domination in graphs. University of Haifa, pp. 1-7.

E.L. Enriquez. (2020). Fair restrained domination in graphs. International Journal of Mathematics Trends and Technology, 66(1), 229-235.

E.L. Enriquez. (2020). Fair secure domination in graphs. International Journal of Mathematics Trends and Technology, 66(2), 49-57.

E.L. Enriquez. (2019). Super fair dominating set in graphs. Journal of Global Research in Mathematical Archives, 6(2), 8-14.

E.L. Enriquez & G.T. Gemina. (2020). Super fair domination in the corona and lexicographic product of graphs. International Journal of Mathematics Trends and Technology, 66(4), 203-210.

G.T. Gemina & E.L. Enriquez. (2020). Super fair dominating set in the cartesian product of graphs. International Journal of Engineering and Management Research, 10(3), 7-11.

E.J. Cockayne, O. Favaron & C.M. Mynhardt. (2003). Secure domination, weak Roman domination and forbidden subgraphs. Bull. Inst. Combin. Appl., 39, 87-100.

E.L. Enriquez & S.R. Canoy, Jr. (2015). Secure convex domination in a graph. International Journal of Mathematical Analysis, 9(7), 317-325.

E.L. Enriquez. & S.R. Canoy, Jr. (2015). Secure convex dominating sets in products of graphs. Applied Mathematical Sciences, 9(56), 2769-2777.

M.P. Baldado, Jr. & E.L. Enriquez. (2017). Super secure domination in graphs. International Journal of Mathematical Archive, 8(12), 145-149.

E.L. Enriquez & E.M. Kiunisala. (2016). Inverse secure domination in graphs. Global Journal of Pure and Applied Mathematics, 12(1), 147-155.

E.M. Kiunisala & E.L. Enriquez. (2016). On clique secure domination in graphs. Global Journal of Pure and Applied Mathematics, 12(3), 2075-2084.

E.L. Enriquez. (2015). Secure convex dominating sets in corona of graphs. Applied Mathematical Sciences, 9(120), 5961-5967.

C.M. Loquias & E.L. Enriquez. (2016). On secure convex and restrained convex domination in graphs. International Journal of Applied Engineering Research, 11(7), 4707-4710.

E.L. Enriquez. (2017). Secure restrained convex domination in graphs. International Journal of Mathematical Archive, 8(7), 1-5.

E.M. Kiunisala & E.L. (2016). Enriquez, inverse secure restrained domination in the join and corona of graphs. International Journal of Applied Engineering Research, 11(9), 6676-6679.

E.L. Enriquez & Evelyn Samper-Enriquez. (2019). Convex secure domination in the join and cartesian product of graphs. Journal of Global Research in Mathematical Archives, 6(5), 1-7.

Published
2020-06-30
How to Cite
Lorelyn P. Gomez, & Enrico L. Enriquez. (2020). Fair Secure Dominating Set in the Corona of Graphs. International Journal of Engineering and Management Research, 10(3), 115-120. https://doi.org/10.31033/ijemr.10.3.18
Section
Articles