The Identifying Code problem on $P_4$-tidy graphs

In this paper we first analyze the behaviour of the identifying code number under union and join operations in graphs. This study forced us to analyze three new parameters related to identifying codes, dominating sets and total dominating sets of the complementary graph. We obtain closed formulas for these parameters on spider and quasi-spider graphs. These results easily derive in a linear dynamic programming-based algorithm for the Identifying Code problem for $P_4$-tidy graphs.