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<正>The Simultaneous Fractional Dimension of Graph Families Cong X.KANG Iztok PETERIN Eunjeong YI Abstract For a connected graph G with vertex set V,let RG{x,y}={z∈V:dG(x,z)≠dG(y,z)}for any distinct x,y∈V,where dG(u,w) denotes the length of a shortest uw-path in G.For a real-valued function g defined on V,let g(V)=∑s∈V g(s).Let C={G1,G2,...,Gk}be a family of connected graphs having a common vertex set V,where k≥2 and|V|≥3.A real-valued function h:V→[0,1] is a simultaneous resolving function of C if h(RG(x,y})≥1for any distinct vertices x,y∈V and for every graph G∈C.The simultaneous.
