Local Distance Antimagic Vertex Coloring of Graphs

A bijective function \(f:V\rightarrow\left\{1,2,3,...,|V| \right\}\) is said to be a local distance antimagic labeling of a graph \(G=(V,E)\), if \(w(u)\neq w(v)\) for any two adjacent vertices \(u, v\) where the weight \(w(v)=\sum_{z\in N(v)}f(z)\). The local distance antimagic labeling of \(G\) induces a proper coloring in \(G\), called local distance antimagic chromatic number denoted by \(\chi_{ld}(G)\). In this article, we introduce the parameter \(\chi_{ld}(G)\) and compute the local distance antimagic chromatic number of graphs. Keywords: Distance antimagic labeling, Local distance antimagic labeling, Local distance antimagic chromatic number.