On Maximum Uniform Partition of Line Graphs
Shuji Shiraishi · QIR (Kyushu University Institutional Repository) (Kyushu University) · 1990
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.