Total outer-convex domination number of graphs

Document Type : Original paper


University of San Jose-Recoletos


In this paper, we initiate the study of total outer-convex domination as a new variant of graph domination and we show the close relationship that exists between this novel parameter and other domination parameters of a graph such as total domination, convex domination, and outer-convex domination. Furthermore, we obtain general bounds of total outer-convex domination number and, for some particular families of graphs, we obtain closed formulas.


Main Subjects

[1] H. Abdollahzadeh Ahangar, F. Fujie-Okamoto, and V. Samodivkin, On the forcing connected geodetic number and the connected geodetic number of a graph, Ars Combin. 126 (2016), 323–335.
[2] H. Abdollahzadeh Ahangar, S. Kosari, S.M. Sheikholeslami, and L. Volkmann, Graphs with large geodetic number, Filomat 29 (2015), no. 6, 1361–1368.
[3] H. Abdollahzadeh Ahangar and M. Najimi, Total restrained geodetic number of graphs, Iran. J. Sci. Technol. Trans. A Sci. 41 (2017), no. 2, 473–480.
[4] H. Abdollahzadeh Ahangar, V. Samodivkin, S.M. Sheikholeslami, and A. Khodkar, The restrained geodetic number of a graph, Bull. Malays. Math. Sci. Soc. 38 (2015), no. 3, 1143–1155.
[5] G. Chartrand and P. Zhang, Convex sets in graphs, Congr. Numer. 136 (1999), 19–32.
[6] J.A. Dayap, R. Alcantara, and R. Anoos, Outer-weakly convex domination number of graphs, Commun. Comb. Optim. 5 (2020), no. 2, 207–215.
[7] J.A. Dayap and E.L. Enriquez, Outer-convex domination in graphs, Discrete Math. Algorithms Appl. 12 (2020), no. 1, Article ID. 2050008.
[8] P. Gupta, Domination in graph with application, Indian J. Res. 2 (2013), no. 3, 115–117.
[9] F. Harary and J. Nieminen, Convexity in graphs, J. Differ Geom. 16 (1981), no. 2, 185–190.
[10] S.T. Hedetniemi and R.C. Laskar, Topics on domination, Elsevier, 1991.
[11] Z. Shao, S. Kosari, R. Anoos, S.M. Sheikholeslami, and J.A. Dayap, Outer-convex dominating set in the corona of graphs as encryption key generator, Complexity 2020 (2020), Article ID. 8316454.