On real number distance labelings of paths (Q2885010)

Let \(G=(V,E)\) be a graph and \(d_{1},\dots,d_{s}\in\mathbb{R}_{\geq 0}\). NEWLINEThen a function \(f:V\rightarrow\mathbb{R}_{\geq 0},\) such that NEWLINE\(\left| f(u)-f(v)\right| \geq d_{k}\) for any two vertices \(u,v\in V\) NEWLINEwith \(d_{G}(u,v)=k\), \(1 \leq k \leq s\) is called a \( L(d_{1},\dots,d_{s})\) labeling of \(G\). NEWLINEIn the paper \(L(d_{1},d_{2},d_{3})\) labelings of paths are studied.