International Journal of Mathematics Trends and Technology
Volume 67 | Issue 7 | Year 2021 | Article Id. IJMTT-V67I7P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I7P516
Let G =(V(G), E(G)) be a connected simple graph. A subset S of V(G) is a dominating set of G if for every u ε V(G) \ S, there exists v ε S such that uv E(G). A dominating set S is an inverse dominating set with respect to a minimum dominating set D of G if S ⊆ V(G) \ D. An inverse dominating set S is called a super inverse dominating set of G if for every vertex u ε V(G) S, there exists v ε S such that NG(v) ∩ (V(G) \ S) = {u}. In this paper, we investigate the concept of super inverse dominating set and give the domination number of some special graphs.
[1] G. Chartrand and P. Zhang. A First Course in Graph Theory, Dover Publication, Inc., New York., (2012).
[2] Ore O., Theory of Graphs, American Mathematical Society, Provedence, R.I., (1962).
[3] Dayap, J.A. and Enriquez, E.L., Outer-convex domination in graphs, Discrete Mathematics, Algorithms and Applications, 12(01) (2020) 2050008.
[4] Enriquez, E.L. and Ngujo, A.D., Clique doubly connected domination in the join and lexicographic product of graphs, Discrete Mathematics, Algorithms and Applications, 12(05) (2020) 2050066.
[5] Enriquez, E.L. and Canoy,Jr., S.R., On a Variant of Convex Domination in a Graph, International Journal of Mathematical Analysis, 9(32) (2015) 1585-1592.
[6] G.M. Estrada, C.M. Loquias, E.L. Enriquez, and C.S. Baraca, Perfect Doubly Connected Domination in the Join and Corona of Graphs, International Journal of Latest Engineering Research and Applications, 4(7) (2019) 11-16.
[7] E.L. Enriquez, V. Fernandez, Teodora Punzalan, and Jonecis Dayap, Perfect Outer-connected Domination in the Join and Corona of Graphs, Recoletos Multidisciplinary Research Journal, 4(2) (2016) 1-8.
[8] Enriquez, E.L., Fair Restrained Domination in Graphs, International Journal of Mathematics Trends and Technology, 66(1) (2020) 229-235.
[9] Galleros, DH.P. and Enriquez, E.L., Fair Restrained Dominating Set in the Corona of Graphs, International Journal of Engineering and Management Research, 10(03) 110-114.
[10] Enriquez, E.L. and Canoy,Jr. S.R., Secure Convex Domination in a Graph, International Journal of Mathematical Analysis, 9(7) (2015) 317-325.
[11] E.L. Enriquez, Fair Secure Domination in Graphs, International Journal of Mathematics Trends and Technology, 66(2) (2020) 49-57.
[12] Gomez, L.P. and Enriquez, E.L., Fair Secure Dominating Set in the Corona of Graphs, International Journal of Engineering and Management Research, 10(03) (2020)115-120.
[13] M.P. Baldado, G.M. Estrada, and E.L. Enriquez, Clique Secure Domination in Graphs Under Some Operations, International Journal of Latest Engineering Research and Applications, 3(6) (2018) 8-14.
[14] C.M. Loquias, and E.L. Enriquez, On Secure Convex and Restrained Convex Domination in Graphs, International Journal of Applied Engineering Research, 11(7) (2016) 4707-4710.
[15] Lemanska, M., Swaminathan, V., Venkatakrishnan, Y. B., Zuazua, R., Super Dominating sets in graphs. Proceedings of the National Academy of Sciences, 85(3) (2015) 353-357.
[16] M.P. Baldado Jr, E.L. Enriquez, Super secure domination in graphs, International Journal of Mathematical Archive, 8 (12) (2017), 145-149.
[17] E.L. Enriquez, Super Convex Domination in the Corona of Graphs, International Journal of Latest Engineering Research and Applications (IJLERA), ISSN: 2455-7137, 3(5) (2018) 1-6.
[18] E.L. Enriquez, Super Restrained Domination in the Corona of Graphs, International Journal of Latest Engineering Research and Applications (IJLERA), ISSN: 2455-7137, 4(7) (2019) 11-16.
[19] E.L. Enriquez, R.A. Bacalso, Super Weakly Convex Domination in Graphs, Journal of Global Research in Mathematical Archives, 6(11) (2019) 1-7.
[20] B.P. Fedellaga, E.L. Enriquez, C.M. Loquias, G.M. Estrada, M.L. Baterna, Super Connected Domination in Graphs, 6(8) (2019) 1-7.
[21] E.L. Enriquez, G.T. Gemina, Super Fair Domination in the Corona and Lexicographic Product of Graphs, International Journal of Mathematics Trends and Technology (IJMTT), 66(4) (2020) 203-210.
[22] G.T. Gemina, E.L. Enriquez, Super Fair Dominating Set in the Cartesian Product of Graphs, International Journal of Engineering and Management Research, 10(3) (2020) 7-11.
[23] E.L. Enriquez, Super Fair Dominating Set in Graphs, Journal of Global Research in Mathematical Archives, 6(2) (2019) 8-14.
[24] V.R. Kulli and S.C. Sigarkanti, Inverse domination in graphs, Nat.Acad. Sci. Letters, 14 (1991) 473-475.
[25] E.L. Enriquez, E.M. Kiunisala, Inverse Secure Domination in the Join and Corona of Graphs, Global Journal of Pure and Applied Mathematics, 12(2) (2016) 1537-1545.
[26] T.J. Punzalan, E.L. Enriquez, Inverse Restrained Domination in Graphs, Global Journal of Pure and Applied Mathematics, 12(3) (2016) 2001-2009.
[27] E.L. Enriquez, E.M. Kiunisala, Inverse Secure Domination in Graphs, Global Journal of Pure and Applied Mathematics, 12(1) (2016) 147-155.
[28] Salve, D.P. and Enriquez, E.L., Inverse Perfect Domination in the Composition and Cartesian Product of Graphs, Global Journal of Pure and Applied Mathematics, 12(1) (2016) 1-10.
[29] C.M. Loquias, E.L. Enriquez, J.A. Dayap, Inverse Clique Domination in Graphs, Recoletos Multidisciplinary Research Journal, 4(2) (2016) 21-32.
[30] Kiunisala, E.M. and Enriquez, E.L., Inverse Secure Restrained Domination in the Join and Corona of Graphs, International Journal of Applied Engineering Research, 11(9) (2016) 6676-6679.
[31] M. Kiunisala, and E.L. Enriquez, Inverse Secure Restrained Domination in the Join and Corona of Graphs, International Journal of Applied Engineering Research, 11(9) (2016) 6676-6679.
[32] J.A. Dayap and E.L. Enriquez, Disjoint Secure Domination in the Join of Graphs, Recoletos Multidisciplinary Research Journal, 4(2) (2016) 9-20.
[33] D.P. Salve and E.L. Enriquez, Inverse Perfect Domination in Graphs, Global Journal of Pure and Applied Mathematics,12(1) (2016) 1-10.
[34] R.C. Alota and E.L. Enriquez, On Disjoint Restrained Domination in Graphs, Global Journal of Pure and Applied Mathematics, 12(3) (2016) 2385-2394.
James A. Ortega, Enrico L. Enriquez, "Super Inverse Domination in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 7, pp. 135-140, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I7P516
PDF 
Abstract 
Keywords 
References 
Citation