An algorithm with a delay of O(kΔ) for enumerating connected induced subgraphs of size k

The problem of enumerating connected subgraphs of a given size in a graph has been extensively studied in recent years. In this short communication, we propose an algorithm with a delay of O(kΔ) for enumerating all connected induced subgraphs of size k in an undirected graph $G=(V, E)$, where k and Δ are respectively the size of subgraphs and the maximum degree of G. The proposed algorithm improves upon the current best delay bound O(k²Δ) for the connected induced subgraph enumeration problem in the literature.