Chartrand, Gary; Johnson, Mark; Oellermann, Ortrud R. Connected graphs containing a given connected graph as a unique greatest common subgraph. (English) Zbl 0611.05056 Aequationes Math. 31, 213-222 (1986). A greatest common subgraph of two nonisomorphic graphs \(G_ 1\) and \(G_ 2\) of equal size is any graph of maximum size without isolated vertices that is a subgraph of both \(G_ 1\) and \(G_ 2\), see i.e. G. Chartrand, F. Saba and H. Zou [Čas. Pěstování Mat. 110, 87-91 (1985; Zbl 0567.05044)]. Here the authors determine those connected graphs G for which there exist nonisomorphic connected graphs of equal size with G as a unique greatest common subgraph. Analogous results are proved for induced subgraphs and subdigraphs. Reviewer: M.Hager Cited in 3 Documents MSC: 05C99 Graph theory 05C40 Connectivity 05C20 Directed graphs (digraphs), tournaments Keywords:greatest common subgraph; induced subgraphs; subdigraphs Citations:Zbl 0567.05044 PDFBibTeX XMLCite \textit{G. Chartrand} et al., Aequationes Math. 31, 213--222 (1986; Zbl 0611.05056) Full Text: DOI EuDML References: [1] Behzad, M., Chartrand, G. andLesniak-Foster, L.,Graphs and digraphs. Wadsworth International, Belmont, CA 1979. · Zbl 0403.05027 [2] Chartrand, G., Saba, F. andZou, H.,Edge rotations and distances between graphs. Časopis Pěst. Math.110 (1985), 87–91. [3] Chartrand, G., Saba, F. andZou, H.,Greatest common subgraphs of graphs. (submitted for publication). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.