Distance $r$-domination number and $r$-independence complexes of graphs

Priyavrat Deshpande, Samir Shukla, Anurag Singh

For $r\ge 1$, the $r$-independence complex of a graph $G$, denoted Ind${}_r(G)$, is a simplicial complex whose faces are subsets $A\subseteq V(G)$ such that each component of the i…