The proposed scheme uses y-coordinates of the points on an ordered EC

isomorphic to the given ordered MEC.

The C*-algebra [T.sup.(n).sub.-[infinity],[infinity]] is isometrically

isomorphic to the C*-algebra [K.sup.H.sub.n] generated by [G.sup.H.sub.n].

[G.sub.[??]] is

isomorphic to [G.sub.F] [??] [S.sub.n/k] as groups, in which the matrix [??] has the form given in Lemma 3.

The impact of geographic distance on the

isomorphic diffusion is not significant except for the central region, while for some poor cities in the western region a negative correlation between these two variables exists.

* The endomorphism monoid of a group G is

isomorphic to the endomorphism monoid of [C.sub.3] x [A.sub.4] if and only if G = [C.sub.3] x [A.sub.4] or G = [C.sub.3] x B, where B is the binary tetrahedral group.

[G.sub.u,n] is the disjoint union of m = [absolute value of ([GAMMA]: [[GAMMA].sub.0] (n))]

isomorphic copies of [F.sub.u,n], where [absolute value of ([GAMMA] : [[GAMMA].sub.0] (n))] is the index of the subgroup [[GAMMA].sub.0] (n) in the group r.

As [G.sub.1] is an m-polar fuzzy graph which is weak

isomorphic with G2, then there exists a weak isomorphism h: [G.sub.1] [right arrow] [G.sub.2] which is bijective for i = 1,2,..., m that satisfies

Thus if the signed graph has odd degree vertices then the 2-path product graphs of S and [eta](S) are not

isomorphic, which is a contradiction.

Assume that G is

isomorphic to [mathematical expression not reproducible].

Then A is

isomorphic to the quotient algebra K[x,y]/([x.sup.n],[y.sup.n]) of the polynomial algebra K[x,y] modulo the ideal ([x.sup.n],[y.sup.n]) generated by [x.sup.n] and [y.sup.n].

Thus [v.sub.1][u.sub.1], [v.sub.3][u.sub.1] [member of] E([bar.G]) and hence G is

isomorphic to [P.sub.4] (2) .

(iv) [Q.sub.h](111)[W(1,1) | W(2,1)] is

isomorphic to [Q.sub.h]-3(111).