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Balaban 10-cage : ウィキペディア英語版 | Balaban 10-cage
In the mathematical field of graph theory, the Balaban 10-cage or Balaban (3,10)-cage is a 3-regular graph with 70 vertices and 105 edges named after A. T. Balaban. Published in 1972,〔A. T. Balaban, A trivalent graph of girth ten, J. Combin. Theory Ser. B 12, 1-5. 1972.〕 It was the first (3,10)-cage discovered but is not unique.〔Pisanski, T.; Boben, M.; Marušič, D.; and Orbanić, A. "The Generalized Balaban Configurations." Preprint. 2001. ().〕 The complete list of (3-10)-cage and the proof of minimality was given by O'Keefe and Wong.〔M. O'Keefe and P.K. Wong, A smallest graph of girth 10 and valency 3, J. Combin. Theory Ser. B 29 (1980) 91–105.〕 There exists 3 distinct (3-10)-cages, the other two being the Harries graph and the Harries–Wong graph.〔Bondy, J. A. and Murty, U. S. R. Graph Theory with Applications. New York: North Holland, p. 237, 1976.〕 Moreover, the Harries–Wong graph and Harries graph are cospectral graphs. The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Balaban 10-cage」の詳細全文を読む
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