More on almost self-complementary graphs |
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Authors: | Nevena Franceti? |
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Institution: | a Department of Mathematics, University of Toronto, Canada b Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Avenue, Ottawa, ON K1N 6N5, Canada |
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Abstract: | A graph X is called almost self-complementary if it is isomorphic to one of its almost complements , where denotes the complement of X and I a perfect matching (1-factor) in . If I is a perfect matching in and is an isomorphism, then the graph X is said to be fairly almost self-complementary if φ preserves I setwise, and unfairly almost self-complementary if it does not.In this paper we construct connected graphs of all possible orders that are fairly and unfairly almost self-complementary, fairly but not unfairly almost self-complementary, and unfairly but not fairly almost self-complementary, respectively, as well as regular graphs of all possible orders that are fairly and unfairly almost self-complementary.Two perfect matchings I and J in are said to be X-non-isomorphic if no isomorphism from X+I to X+J induces an automorphism of X. We give a constructive proof to show that there exists a graph X that is almost self-complementary with respect to two X-non-isomorphic perfect matchings for every even order greater than or equal to four. |
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Keywords: | Almost self-complementary graph Perfect matching Connected graph Regular graph Fairly almost self-complementary graph Unfairly almost self-complementary graph |
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