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∈ V(G) resolves X and Y if dG(v,X)≠ dG(v,Y)‎, ‎where dG(v,X) (or dG(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 ‎, ‎Y\ is denoted by RG,Y\‎.‎A real valued function g‎: ‎V(G)→ [0‎, ‎1] is a k-clique resolving function of G if ∑_v∈ RG,Y(v)≥ 1 for each two distinct k-cliques X and Y of G‎. ‎The fractional k-clique metric dimension of G is defined as‎‎k-cdimf(G)=min\|g|\‎, :\, ‎g \; is a\; k-clique resolving function of\; G\‎, ‎where |g|=∑v∈ 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-cdimf of (edge) corona products of graphs‎.