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

  • E J 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 7! {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

Keywords: Domination, dominating function, s-dominating r-function.

ORiON Vol. 23 (1) 2007: pp. 51-58
Published
2008-01-14
Section
Articles

Journal Identifiers


eISSN: 0529-191-X