\(L(2,1)\)-labeling for subdivisions of cycle dominated graphs
Summary: Let \(G(V,E)\) be a simple, finite, connected, undirected graph. Distance two labeling or \(L(2,1)\)-labeling of a graph \(G\) is an assignment \(f\) from the vertex set \(V(G)\) to the set of non-negative integers such that \(| f(x)-f(y)| \geq 2\) if \(x\) and \(y\) are adjacent and \(| f(x)-f(y)| \geq 1\) if \(x\) and \(y\) are at distance 2, for all \(x\) and \(y\) in \(V(G)\). The \(L(2,1)\)-labeling number \(\lambda(G)\) of \(G\) is the smallest number \(k\) such that \(G\) has an \(L(2,1)\)-labeling \(f\) with \(\max\{f(v):v\in V(G)\}=k\). In this paper, we construct \(L(2,1)\)-labeling of subdivisions of cycle dominated graphs like subdivided Double Fans, subdivided \(nC_\alpha\) with a common vertex and subdivided Books \(B_n\) and hence we find the \(\lambda\)-number of these graphs.
scientific article; zbMATH DE number 6914247
scientific article