By Jost J., Xin Y. L.

We receive a Bernstein theorem for distinct Lagrangian graphs in for arbitrary merely assuming bounded slope yet no quantitative limit.

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**Extra info for A Bernstein theorem for special Lagrangian graphs**

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10. 7: No. 24) this product of No. 22 and this group group is is the the direct direct product of No. 26) gives aa hamiltonian hamiltonian circuit circuit with with the the non-antipalindromic non-antipalindromic LCF LCF gives code code 18 [5,-29,29,43,-43,-5]18 .. 8: No. 27) It been mentioned-see It has has already already been mentioned—see Remark Remark (iv) (iv) at at the the end end of of Section Section 7-that 7—that the the groups groups Z(11,5,2) Z (11,5,2) and and Z(11,5,8) Z (11,5,8) are are abstractly being isomorphic abstractly isomorphic isomorphic (both (both being isomorphic to to the the Zero-Symmetric Zero-Symmetric Graphs Graphs 46 K-metacyclic p = 11); but the K-metacyclic group group for for p 1 1 ) ; but the Cayley Cayley graphs graphs 8A 8A and and 8B be different because of 8B turn turn out out to to be different because of the the difference difference in in generators.

1) (1 (1 <<_ kk << m) m) where, be consistent, where, in in order order for for these these relations relations to to be consistent, k k must must satisfy satisfy s kk S _E 11 (mod (mod m) m) .. 1) when when m m = = p is aa prime, = p 1, and and k k is is arising p is prime, ss = p -- 1, primitive root root (mod (mod p). p). 5), where where we we saw saw that that the the same same group group countered before in could be generated by one involutory involutory and and one one non-involutory non-involutory could be generated by one element, thus thus leading leading to to aa trivalent trivalent Cayley Cayley graph.

1) Four more more such such cases cases have have been been encountered encountered above, above, namely; Four namely; 2 , 11 2 1 -1 (i) (i) No. 1: Z(5,2,2) = - F F " '" No. 1: Z(9,3,2) = F F" No. 1: Z{5,6,2) = F F" No. 1: Z(5,6,2) (iv) (iv) No. 8A/8B No. 1: Z(ll,5,2) Z(ll,5,2) = = F F '' ', - - 31 1 3 1 -1 3 or order order 20; 20; or of order order 54; 54; of ,1 2 3 2 1 - , of order order 60; 60; of 4 2 1 43 2 4 2 1 = - 4 ' 3 , -2 = FF ' '" of 110. of order order 110. 9), and and two two of 33 2 -1 and F 44 ,2,1, 2 1 them, them, F F ,2,-1 ' ' and F ' ' , will will be be considered considered in in this this section section because because they they have have O-symmetric O-symmetric Cayley Cayley graphs graphs with with fewer fewer than than 120 120 vertices.

### A Bernstein theorem for special Lagrangian graphs by Jost J., Xin Y. L.

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