k-tuple and k-tuple total dominations on web graphs

Abstract

In this work we address k-tuple and k-tuple total dominations on the subclass of circular-arc graphs given by web graphs. For the non total version, we present a linear time algorithm based on the regularity of the closed neighborhoods associated with web graphs which allows the use of modular arithmetic for integer numbers. For the total version, we derive bounds for this graph class. PreliminariesDomination in graphs is useful in different applications. There exist many variations -such as k-tuple domination and k-tuple total domination, among others-regarding slight differences in their definitions. These differences make circular-arc graph subclasses adequate and useful mostly due to their relation to "circular" issues, such as in forming sets of representatives, in resource allocation in distributed computing systems,