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We show that (A) If G = (V, E) is an Euler circuit, then the number of the maximum uniform partition of the line graph L(G) is (1/4) $ Sigma _ upsilon \varepsilon \u d^2_\u$ (-l)(-1 is added when mid... E mid is odd), where $d_nu$, is the degree of v. (B) If G is not an Euler circuit, then the number of the maximum uniform partition of L(G) is (1/4) $ Sigma _ upsilon \varepsilon \u d^2_\u - iota $, where $ iota $ is the number of vertices of odd degree.show more
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