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The connectivity of squares of box graphs. (English) Zbl 1126.05062
Summary: This paper copies results that were obtained a long time ago. What the authors call box graphs is what other authors call subdivision graphs. In the present paper the authors study the square of a box graph, but it has been proved that this square is the well-known total graph [M. Behzad, Proc. Camb. Philos. Soc. 63, 679–681 (1967; Zbl 0158.20703; M.R. 35#2771)]. The connectivity of total graphs has been widely studied in different papers; the results presented in this one can be found in [J. M. S. Simões-Pereira, Math. Ann. 196, 48–57 (1972; Zbl 0218.05077; M.R. 45#8568); D. Bauer and R. Tindell, J. Graph Theory 6, 197–203 (1982; Zbl 0457.05045; M.R. 84d:05113); T. Hamada, T. Nonaka and I. Yoshimura, Math. Ann. 196, 30–38 (1972; Zbl 0215.33802); M.R. 45#5020); M. Behzad, Bull. Austral. Math. Soc. 1, 175–181 (1969; Zbl 0174.26801; M.R. 41#6706)]. For example, Lemmas 2.7, 2.8 and 2.9 are exact copies of Lemmas 1, 2 and 3 in the paper by Simões-Pereira cited above; even more, the phrasing before the lemmas is the same. Moreover, Theorem 3.4 is one of the results of [M. Behzad, op. cit.; (Zbl 0174.26801; M.R. 41#6706)]. I believe that this paper should not have been published.
Reviewd by Angeles Carmona (M.R. 2007h:05087)

MSC:
05C40 Connectivity
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