On the fractional edge dimension of graphs

Let G = (V (G),E(G)) be a connected graph. For any vertex x is an element of V (G) and edge e = yz is an element of E(G), the distance between the vertex x and the edge e = yz is defined as d(x,e) =min{d(x,y),d(x,z)}. A vertex x is an element of V (G) is said to resolve two distinct edges e1,e2 is an element of E(G) if d(x,e(1))not equal d(x,e(2)). Let R{e(1),e(2)} be defined by R{e(1),e(2)} = {x is an element of V (G) : d(x,e(1))not equal d(x,e(2))}. A real valued function f : V (G) -> [0, 1] is an edge resolving function of G if f(R{e(1),e(2)}) >= 1 for any two distinct edges e(1),e(2) is an element of E(G), where f(R{e(1),e(2)}) = Sigma(x is an element of R{e1,e2})f(x). The fractional edge dimension of G is given by edim(f)(G) =min{f(V (G)): f is an edge resolving function of G}, where f(V (G)) = Sigma(x is an element of V) ((G))f(x). In this paper, we study the fractional edge dimension of prism D-n, antiprism An, the web graph W-n, and the triangular winged prism graph TWPn.