Some Results on Inclusive Distance Antimagic Labeling of Graphs

Abstract

Let $G=(V,E)$ be a graph of order $n$. A bijection $f:V(G)\rightarrow \{1,2,\cdots,n\}$ is called inclusive distance antimagic labeling if $w(u)\ne w(v)$ for any two distinct vertices $u,v\in V(G)$, where $w(v) = \displaystyle \sum_{x\in N[v]} f(x)$. We start our discussion with the connection between distance magic labeling and inclusive distance antimagic labeling. Then, we investigate the existence of an inclusive distance antimagic labeling for circulant graphs, disjoint union graphs, and join graphs.