Goddard, Wayne; Swart, Henda C. Integrity in graphs: Bounds and basics. (English) Zbl 0708.05031 J. Comb. Math. Comb. Comput. 7, 139-151 (1990). Summary: The integrity of a graph G, denoted I(G), is defined by \(I(G)=\min \{| S| +m(G-S):\) \(S\subset V(G)\}\) where m(G-S) denotes the maximum order of a component of G-S; further an I-set of G is any set S for which the minimum is attained. Firstly some useful concepts are formalized and basic properties of integrity and I-sets identified. Then various bounds and interrelationships involving integrity and other well- known graphical parameters are considered, and another formulation introduced from which further bounds are derived. The paper concludes with several results on the integrity of circulants. Cited in 12 Documents MSC: 05C35 Extremal problems in graph theory Keywords:integrity of a graph PDFBibTeX XMLCite \textit{W. Goddard} and \textit{H. C. Swart}, J. Comb. Math. Comb. Comput. 7, 139--151 (1990; Zbl 0708.05031)