Fractional k-clique metric dimension of (edge) corona products of graphs

‎Let $G$ be a graph‎, ‎and let $X$ and $Y$ be two cliques of $G$‎. ‎A vertex $v\in V(G)$ resolves $X$ and $Y$ if $d_G(v,X)\neq d_G(v,Y)$‎, ‎where $d_G(v,X)$ (or $d_G(v,Y)$) is the number of edges on a shortest path between $v$ and $X$ (or $v$ and $Y$) in $G$‎.‎The subset of all vertices that resolve the pair $\{X‎, ‎Y\}$ is denoted by $R_G\{X,Y\}$‎.‎A real valued function $g‎: ‎V(G)\rightarrow [0‎, ‎1]$ is a $k$-clique resolving function of $G$ if $\sum_{v\in R_G\{X,Y\}}g(v)\geq 1$ for each two distinct $k$-cliques $X$ and $Y$ of $G$‎. ‎The fractional $k$-clique metric dimension of $G$ is defined as‎‎$k$-${\rm cdim}_f(G)=\min\{|g|\‎, :\, ‎g \; \text{is a}\; k\text{-clique resolving function of}\; G\}$‎, ‎where $|g|=\sum_{v\in V(G)}g(v)$‎.‎In this paper‎, ‎we introduce and study the fractional $k$-clique metric dimension of graphs as an approximation of $k$-clique metric dimension that has applications in robot navigation‎. ‎We also determine $k$-${\rm cdim}_f$ of (edge) corona products of graphs‎.