Restrained and Total Restrained Domination of Ladder Graphs

Authors

DOI:

https://doi.org/10.26713/cma.v14i4.2569

Keywords:

Domination, Total domination, Restrained domination

Abstract

Telle and Proskurowksi introduced restrained domination as a vertex partition problem in partial \(k\)-tress (Algorithms for vertex partitioning problems on partial \(k\)-trees, SIAM Journal on Discrete Mathematics 10(4) (1997), 529 - 550). For a graph \(G(V,E)\), a restrained domination number is the minimum cardinality of a subset \(\mathfrak{D}\) of \(V\) such that for every vertex \(v\in \bar{\mathfrak{D}}\) there is a vertex in \(\mathfrak{D}\) as well as in \(\bar{\mathfrak{D}}\) adjacent to \(v\). If \(\mathfrak{D}\) satisfies an additional condition that every vertex of \(V\) has a neighbor in \(\mathfrak{D}\), then \(\mathfrak{D}\) is said to be a total restrained dominating set. Minimum cardinality of \(\mathfrak{D}\) is said to be total restrained domination number of graph \(G\). In this paper we have obtained domination, restrained, total and total restrained domination number of some ladder graphs.

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Published

25-12-2023
CITATION

How to Cite

Hemalatha, N. C., Chandrakala, S. B., Sooryanarayana, B., & Kumar, M. V. (2023). Restrained and Total Restrained Domination of Ladder Graphs. Communications in Mathematics and Applications, 14(4), 1311–1323. https://doi.org/10.26713/cma.v14i4.2569

Issue

Vol. 14 No. 4 (2023)

Section

Research Article

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