In-Dominating Number and Out-Dominating Number of Unidirectional Perfect Binary Trees

Sanal Kumar, Jithin Mathew

Abstract


A diverging unidirectional perfect binary tree is a unidirectional perfect binary tree in which every internal node has exactly outdegree two and indegree 1 and all the leaf nodes are at the same level. A converging unidirectional perfect binary tree is a unidirectional perfect binary tree in which every internal node has exactly indegree two and outdegree 1 and all the leaf nodes are at the same level. In this paper, we study the out-domination number and in-domination number of the unidirectional perfect binary trees.

Keywords


In-Dominating set; Out-Dominating set; In-Domination number; Out-Domination number; Unidirectional Tree Graph

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References


S. Alikhani, Dominating sets and domination polynomials of graphs. Lap Lambert Academic, 2012.

A. Brandstadt and D. Kratsch, On domination problems for permutation and other graphs, Theoret. Comput. Sci. 54 (1987) 181-198.

D.G. Corneii and Y. Perl, Clustering and domination in perfect graphs, Discrete Appl. Math. 9 (1984) 27-39.

J.F. Couturier, R. Letourneur, and M. Liedloff. On the number of minimal dominating sets on some graph classes. Theoretical Computer Science, 562:634–642, 2015.

G. Chartrand, F. Harary and B. Quan Yue, "On the out-domination and in-domination numbers of a digraph", Discrete mathematics, vol. 197-198, pp. 179-183, 1999.

J. Ghoshal, R. Laskar, and D. Pillone, "Topics on domination in directed graphs," in Domination in graphs advanced topics, T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Eds. New York, NY: Routledge, 1998, pp. 401-437.

J. Ghosal, R. Laskar, and D. Pillone. Topics on domination in directed graphs, Marcel Dekker, New York, 1998.

T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of domination in graphs. New York, NY: CRC, 1998.

T.W. Haynes, S.T. Hedetniemi, P.J. Slater (Ed.), Domination in Graphs: Advanced Topics, Marcel Dekker, New York, 1998.

P. Paul Hawkins, A.M. Anto 2, T. Shyla Isac Mary, Perfect Dominating sets and Perfect Domination Polynomial of a Pan Graph, Journal Of Critical Reviews ISSN- 2394-5125, vol 7, issue 04, 2020.

C. Pang, R. Zhang, Q. Zhang, and J. Wang, "Dominating sets in directed graphs", Information sciences, vol. 180, no. 19, pp. 3647-3652, 2010.




DOI: http://dx.doi.org/10.21533/scjournal.v12i2.277

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Copyright (c) 2023 Sanal Kumar, Jithin Mathew

ISSN 2233 -1859

Digital Object Identifier DOI: 10.21533/scjournal

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