Exact values for three domination-like problems in circular and infinite grid graphs of small height

Abstract

In this paper we study three domination-like problems, namely identifying codes, locating-dominating codes, and locating-total-dominating codes. We are interested in finding the minimum cardinality of such codes in circular and infinite grid graphs of given height. We provide an alternate proof for already known results, as well as new results. These were obtained by a computer search based on a generic framework, that we developed earlier, for the search of a minimum labeling satisfying a pseudo-d-local property in rotagraphs.

Keywords

• graph algorithm
• identifying code
• locating-dominating code
• locating-total-dominating code
• grid
• acm: g.: mathematics of computing/g.2: discrete mathematics/g.2.2: graph theory
• acm: g.: mathematics of computing/g.2: discrete mathematics/g.2.2: graph theory/g.2.2.0: graph algorithms
• acm: g.: mathematics of computing/g.2: discrete mathematics/g.2.2: graph theory/g.2.2.1: graph labeling
• acm: g.: mathematics of computing/g.2: discrete mathematics/g.2.2: graph theory/g.2.2.4: path and circuit problems
• [info.info-dm]computer science [cs]/discrete mathematics [cs.dm]