文摘
Bond (1987) and Bond et al. (1987), conjectured that a quasi-center in an undirected de Bruijn graph X15004400&_mathId=si1.gif&_user=111111111&_pii=S0166218X15004400&_rdoc=1&_issn=0166218X&md5=d415942995d4bd40a37d7c930d1e606e" title="Click to view the MathML source">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 15e131bc3a9c817316a2672879" title="Click to view the MathML source">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 15e131bc3a9c817316a2672879" title="Click to view the MathML source">UB(2,D) is D−1), and give simplified proofs of the cited results.