Some conditions for n-extendable graphs

Abslracl A Tulle slyle necessary and surricienl condilion lor n-ex'lendable graphs is proposed. Lel G be a conn-ecled graph and lel u and v be lwo verlices or G such lhal dGCu,v) == 2. We derine divergenceex*Cu.v) as an independenl sel conlaining u and v in G[{w) U NGCw)]) * aI'ld ex Cu, v) = max { I Cw) w U,v proved lhal ir ror any lwo verlices u and v or G such 1 and ir G has even order, lhen G is I'l-ex'lendable. Il is also proved lhal ir ror each v in VCG) , G' = G({v) U NGCv)] and ~CG') ~ exCG') + 2n-1 and ir G has even order. lhen G is n-ex'lendable.