If [phi] is a refined neutrosophic
bijective homomorphism then it is called refined neutrosophic isomorphism and we write RNQ(H) = RNQ(J).
Moreover, X denotes AddRoundKey, and S represents the
bijective nonlinear mapping, i.e., S(a) = S([a.sub.15] [parallel] [a.sub.14] [parallel] [a.sub.13] *** [parallel] [a.sub.2] [parallel] [a.sub.1] [parallel] [a.sub.0]) = [b.sub.15] [parallel] [b.sub.14] [parallel] [b.sub.13] *** [parallel] [b.sub.2] [parallel] [b.sub.1] [parallel] [b.sub.0], where [b.sub.i] = [pi]([a.sub.i])(0 < i < 15).
Let [phi] : X [right arrow] Y be a
bijective function and (B, [B.sup.*]) be an (L,M)-dffb on Y.
Then by the same discussion as the proof of Proposition 15 in Case 1, we have [S.sup.r]([rho]) = [S.sup.r]([phi]([rho])), [phi]([P.sub.1](H)) = [P.sub.1](H), and that [phi] is a
bijective map which preserves orthogonality in both directions.
Yu, "Efficient unicast in
bijective connection networks with the restricted faulty node set," Information Sciences, vol.
Indeed, it is easy to see that the family of
bijective linear functions [R.sup.m] [right arrow] [R.sup.m] is l-lineable if and only if there are
bijective linear functions [f.sub.1],..., [f.sub.l] : [R.sup.m] [right arrow] [R.sup.m] such that, for every x [member of] [R.sup.m] \ {0}, the set {[f.sub.1](x),..., [f.sub.l](x)} is a linearly independent system.
A fuzzy graph (Eq.) is knows as a fuzzy magic graph if there exist two
bijective functions (Eq.) and (Eq.) ]such that (Eq.) and (Eq.) for all (Eq.) where (Eq.) is a fuzzy magic constant.