The general sum-connectivity index of a graph $G$ is defined as $chi_{alpha}(G)= sum_{uvin E(G)} (d_u + d_{v})^{alpha}$ where $d_{u}$ is degree of the vertex $uin V(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $chi_{alpha}$ values from a certain collection of polyomino ...

Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency a highest-degree branching algorithm with degree-based pruning. In this paper, we prove that empirically fast runs in $$O(3.460^k n)$$ time, where k is solution size. This improves previous best $$O(3.619^k -time deterministic obtained by Kociumaka and Pilipczuk (Inf Process Lett 114:556–56...