On lower bounds of various dominating codes for locating vertices in cubic graphs

Abstract

Self-identifying codes, self-locating dominating codes and solid-locating dominating codes are three subsets of vertices of a graph G to locate vertices. The optimal size of them is denoted by γSID (G),γSLD (G) and γDLD (G). In the master thesis, we mainly discuss their lower bound problem in families of graphs. In the first section, we briefly describe the background of the study and some related questions. In the second, third and fourth section, we show some basic definitions, concepts and examples related to self-identifying codes (SID), self-locating dominating codes (SLD) and solid-locating dominating codes (DLD) in rook’s graphs. In the fifth section, we first introduce some known results of lower bounds of open-locating dominating codes in cubic graphs and then in the sixth section we present some new results about the lower bounds of self-identifying codes, self-locating dominating codes and solid-locating dominating codes in cubic graphs.