Quasi-centers and radius related to some iterated line digraphs, proofs of several conjectures on de Bruijn and Kautz graphs

摘要

Bond (1987) and Bond et al. (1987), conjectured that a quasi-center in an undirected de Bruijn graph UB(d, D) has cardinality at least d 1, and that a quasi-center in an undirected Kautz graph UK(d, D) has cardinality at least d. They proved that for d >= 3, the radii of UB(d, D) and UK(d, D) are both equals to D, and conjectured also that the radii of UB(2, D) and UK(2, D) are respectively D - 1 and D. In this paper we give results in a more general context which validate these conjectures (excepting that asserting that the radius of UB(2, D) is D - 1), and give simplified proofs of the cited results. (C) 2015 Elsevier B.V. All rights reserved.