An algorithm for the (r,s)-domination number of a tree

EJ Cockayne

Abstract


Suppose that at most r units of some commodity may be positioned at any vertex of a graph G = (V,E) while at least s (>= r) units must be present in the vicinity (i.e. closed neighbourhood) of each vertex. Suppose that the function f : V -> {0,...,r}, whose values are the numbers of units stationed at vertices, satisfies the above requirement. Then f is called an s-dominating r-function. We present an algorithm which finds the minimum number of units required in such a function and a function which attains this minimum, for any tree.

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DOI: https://doi.org/10.5784/23-1-46

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ISSN 2224-0004 (online); ISSN 0259-191X (print)

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