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Further results on graph equations for line graphs and n-th power graphs

Authors:	Jin Akiyama Hiroshi Era Geoffrey Exoo

Institution:	Department of Mathematics, Nippon Ika University, Kawasaki 211, Japan;Department of Mathematics, Tokai University, Hiratsuka, Japan;Department of Mathematics, The University of Michigan, Ann Arbor, MI 48109, U.S.A.

Abstract:	We present solutions of seven graph equations involving the line graph, complement and n-th power operations. One such equation $L(G)^{n} = G ?$ generalizes a result of M. Aigner. In addition, some comments are made about graphs satisfying $G^{n} = G ?$ .

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