Abstract.
Let G=(V,E) be a graph and P={V 1,V 2,…,V k } be a partition of V. The k-complement G k P (with respect to P) is defined as follows: For all V i and V j in P, i≠j, remove the edges between V i and V j , and add the edges which are not in G. A graph G is k-self complementary, if there exists a partition P of order k such that G k P≅G. For 2≤k≤p, characterizations of all k-self complementary trees, forests and connected unicyclic graphs of order p are obtained.
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Received: February 21, 1996 / Revised: October 30, 1996
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Sampathkumar, E., Pushpalatha, L. Complement of a Graph: A Generalization. Graphs Comb 14, 377–392 (1998). https://doi.org/10.1007/PL00021185
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DOI: https://doi.org/10.1007/PL00021185