Computational complexity of domination integrity in graphs - Sundareswaran, R; Swaminathan, V (TWMS journal of applied and engineering mathematics, 2015)
In a graph G, those dominating sets S which give minimum value for |S| + m(G-S), where m(G-S) denotes the maximum order of a component of G-S, are called dominating integrity sets of G (briey called DI-sets of G). This concept combines two important aspects namely domination and integrity in graphs. In this paper, we show that the decision problem domination integrity is NP-complete even when restricted to planar or chordal graphs.