Inverse Perfect Restrained Domination in Graphs

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-8
Year of Publication : 2021
Authors : Hanna Rachelle A. Gohil, Enrico L. Enriquez
  10.14445/22315373/IJMTT-V67I8P519

MLA

MLA Style: Hanna Rachelle A. Gohil, Enrico L. Enriquez  "Inverse Perfect Restrained Domination in Graphs" International Journal of Mathematics Trends and Technology 67.8 (2021):164-170. 

APA Style: Hanna Rachelle A. Gohil, Enrico L. Enriquez(2021). Inverse Perfect Restrained Domination in Graphs  International Journal of Mathematics Trends and Technology, 67(8), 164-170.

Abstract
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 ∈ V(G) \ S, there exists v ∈ S such that uv ∈ E(G). A dominating set S is called a restrained dominating set if for each u ∈ V(G)\S there exist v ∈ S and z ∈ V(G) \ S (z≠u) such that u is adjacent to v and z. A restrained dominating set S is called perfect restrained dominating set of G if each u ∈ V(G) \ S is dominating by exactly one element of S. Further, if D is a minimum perfect restrained dominating set of G, then a perfect restrained dominating set S ⊆ V(G) \ D is called an inverse perfect restrained dominating set of G with respect to D. In this paper, we investigate the concept and give some important results .

Reference

[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 , https://doi.org/10.1142/S1793830920500081
[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] Enriquez, E.L. and Canoy,Jr., S.R., Secure Convex Domination in a Graph, International Journal of Mathematical Analysis, 9(7) (2015) 317-325.
[7] 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 , https://doi.org/10.31033/ijemr.10.3.18.
[8] M.P. Baldado Jr, E.L. Enriquez, Super secure domination in graphs, International Journal of Mathematical Archive, 8 (12) (2017), 145-149.
[9] 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.
[10] E.L. Enriquez, E. Samper-Enriquez, Convex Secure Domination in the Join and Cartesian Product of Graphs, Journal of Global Research in Mathematical Archives, 6(5) (2019) 1-7.
[11] J.A. Telle, A. Proskurowski, Algorithms for Vertex Partitioning Problems on Partial k Trees, SIAM J. Discrete Mathematics, 10(1997) 529-550.
[12] Enriquez, E.L., Fair Restrained Domination in Graphs, International Journal of Mathematics Trends and Technology, 66(1) (2020) 229-235.
[13] 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) (2020) 110-114. https://doi.org/10.31033/ijemr.10.3.17
[14] T.J. Punzalan, and E.L. Enriquez, Restrained Secure Domination in the Join and Corona of Graphs, Journal of Global Research in Mathematical Archives, 5(5) (2018) 1 - 6.
[15] E.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.
[16] 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.
[17] E.L. Enriquez, Secure restrained convex domination in graphs, International Journal of Mathematical Archive, 8(7) (2017) 1-5.
[18] B.F. Tubo and S.R. Canoy, Jr., Restrained Perfect Domination in Graphs, International Journal of Mathematical Analysis, 9(25) (2015) 1231 – 1240.
[19] 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.
[20] D.P. Salve and E.L. Enriquez, Inverse Perfect Domination in Graphs, Global Journal of Pure and Applied Mathematics. ISSN 0973-1768, 12(1) (2016) 1-10.
[21] 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.
[22] V.R. Kulli and S.C. Sigarkanti, Inverse domination in graphs, Nat.Acad. Sci. Letters, 14 (1991) 473 - 475.
[23] E.L. Enriquez, E.M. Kiunisala, Inverse Secure Domination in the Join and Corona of Graphs, Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, 12(2) (2016) 1537-1545.
[24] T.J. Punzalan, E.L. Enriquez, Inverse Restrained Domination in Graphs, Global Journal of Pure and Applied Mathematics. ISSN 0973-1768, 12(3) (2016) 2001 - 2009.
[25] E.L. Enriquez, E.M. Kiunisala, Inverse Secure Domination in Graphs, Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, 12(1) (2016) 147 – 155.
[26] 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.
[27] C.M. Loquias, E.L. Enriquez, J.A. Dayap, Inverse Clique Domination in Graphs, Recoletos Multidisciplinary Research Journal, 4(2) (2016) 21-32.
[28] 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.

Keywords : dominating set, restrained dominating set, perfect restrained dominating set, inverse perfect restrained dominating set