Abstract
In this paper, a new parameter on domination is defined by imposing a restriction on the degrees of vertices in the dominating set. For a positive integer k, a dominating set D of a graph G is said to be a k-part degree restricted dominating set (k-DRD-set), if for all u ∈ D there exists a set C u ⊆ N(u) ∩ (V − D) such that \(|C_u| \leq \lceil \frac {d(u)}{k}\rceil \) and ⋃u ∈ D C u = V − D. The minimum cardinality of a k-part degree restricted dominating set of G is called the k-part degree restricted domination number of G and is denoted by \(\gamma _{\frac {d}{k}}(G)\). Here, we determine the k-part degree restricted domination number of some well-known graphs, relation between dominating and k-DRD set, and an algorithm which verifies whether a given dominating set is a k-DRD set or not.
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Kamath, S.S., Senthil Thilak, A., M, R. (2019). Relation Between k-DRD and Dominating Set. In: Rushi Kumar, B., Sivaraj, R., Prasad, B., Nalliah, M., Reddy, A. (eds) Applied Mathematics and Scientific Computing. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-01123-9_56
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DOI: https://doi.org/10.1007/978-3-030-01123-9_56
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