Distance-transitive antipodal covers: The extremal case. (English) Zbl 0808.05065
Summary: An \(r\)-fold antipodal cover of a distance-regular graph of valency \(k\) always satisfies \(r \leq k\), see the author [J. Comb. Theory, Ser. B 16, 255-273 (1974; Zbl 0267.05111)]. We show that there is no distance- transitive 56-fold antipodal cover of \(K_{57}\), thereby completing the classification of distance-transitive antipodal covering graphs with \(r=k\).
MSC:
| 05C35 | Extremal problems in graph theory |
| 05C12 | Distance in graphs |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
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