Domination and s-path domination in some brick product graphs

Abstract

A dominating set or dset of $\mathscr{G}$ is called a s-path dset of $\mathscr{G}(2 \leq s \leq \operatorname{diam} \mathscr{G})$ if any path of length $s \in \mathscr{G}$ has $\subseteq$ of one vertex in this dset. We indicate a s-path dset by $D_{p_s}$. The s-path dominaton number or s-path dn of $\mathscr{G}$ indicated by $\gamma_{p_s}(\mathscr{G})$ is the minimal cardinality or MC taken over all s-path dsets of $\mathscr{G}$. In that paper, we determine domination number and s-path domination number for the brick product graph $B(2 n, \mathscr{P}, \mathscr{Q})(\mathscr{P}=2)$ related with even cycles.