Summary: A graph \(H\) is a clique graph if \(H\) is a vertex-disjoin union of cliques. F. N. Abu-Khzam [J. Discrete Algorithms 45, 26–34 (2017; Zbl 1419.68056)] introduced the \(( a , d )\)-Cluster Editing problem, where for fixed natural numbers \(a , d\), given a graph \(G\) and vertex-weights \(a^\ast : V ( G ) \to \{ 0 , 1 , \ldots , a \}\) and \(d^\ast : V ( G ) \to \{ 0 , 1 , \ldots , d \}\), we are to decide whether \(G\) can be turned into a cluster graph by deleting at most \(d^\ast ( v )\) edges incident to every \(v \in V ( G )\) and adding at most \(a^\ast ( v )\) edges incident to every \(v \in V ( G )\). Results by C. Komusiewicz and J. Uhlmann [Discrete Appl. Math. 160, No. 15, 2259–2270 (2012; Zbl 1252.05178)] and Abu-Khzam [loc. cit.] provided a dichotomy of complexity (in P or NP-complete) of \(( a , d )\)-Cluster Editing for all pairs \(a\), \(d\) apart from \(a = d = 1 .\) Abu-Khzam [loc. cit.] conjectured that \(( 1 , 1 )\)-Cluster Editing is in P. We resolve Abu-Khzam’s conjecture in affirmative by (i) providing a series of five polynomial-time reductions to \(C_3\)-free and \(C_4\)-free graphs of maximum degree at most 3, and (ii) designing a polynomial-time algorithm for solving \(( 1 , 1 )\)-Cluster Editing on \(C_3\)-free and \(C_4\)-free graphs of maximum degree at most 3.