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  • In 1960, Homan and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d^2+1 vertices), and found that such graphs exist only for d = 2; 3; 7 and possibly 57. In 1980, Erdos et al., using eigenvalue analysis, showed that, with the exception of C_4, there are no graphs of diameter 2, maximum degree d and d^2 vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d^2-1 vertices do not exist for most values of d with d at least 6, and conjecture that they do not exist for any d greater or equal to 6.
  • In 1960, Homan and Singleton investigated the existence of Moore graphs of diameter 2 (graphs of maximum degree d and d^2+1 vertices), and found that such graphs exist only for d = 2; 3; 7 and possibly 57. In 1980, Erdos et al., using eigenvalue analysis, showed that, with the exception of C_4, there are no graphs of diameter 2, maximum degree d and d^2 vertices. In this paper, we show that graphs of diameter 2, maximum degree d and d^2-1 vertices do not exist for most values of d with d at least 6, and conjecture that they do not exist for any d greater or equal to 6. (en)
Title
  • On the nonexistence of graphs of diameter 2 and defect 2
  • On the nonexistence of graphs of diameter 2 and defect 2 (en)
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  • On the nonexistence of graphs of diameter 2 and defect 2
  • On the nonexistence of graphs of diameter 2 and defect 2 (en)
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  • RIV/49777513:23520/09:00503074!RIV10-MSM-23520___
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  • 331555
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  • RIV/49777513:23520/09:00503074
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  • Moore graphs; degree/diameter problem; diameter 2 and defect (en)
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  • CA - Kanada
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  • Journal of Combinatorial Mathematics and Combinatorial Computing
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  • 71
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  • Miller, Mirka
  • Pineda-Villavicencio, Guillermo
  • Nguyen, Minh Hoang
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  • 0835-3026
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  • 23520
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