If $\mathcal{P}$ is a given graph property. we say that a graph $G$ is locally $\mathcal{P}$ if $\langle N(v) \rangle$ has property $\mathcal{P}$ for every $v \in V(G)$ where $\langle N(v) \rangle$ is the induced graph on the open neighbourhood of the vertex $v$. Pareek and Skupien (C. M. https://www.socialstudiesscholar.com/