Endomorphisms and cores of quadratic forms graphs in odd characteristic |
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Institution: | School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, 410004, China |
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Abstract: | A graph G is called a pseudo-core if every endomorphism of G is either an automorphism or a colouring. A graph G is a core if every endomorphism of G is an automorphism. Let be the finite field with q elements where q is a power of an odd prime number. The quadratic forms graph, denoted by where , has all quadratic forms on as vertices and two vertices f and g are adjacent whenever or 2. We prove that every is a pseudo-core. Further, when n is even, is a core. When n is odd, is not a core. On the other hand, we completely determine the independence number of . |
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Keywords: | Quadratic forms graph Endomorphism Pseudo-core Core Maximal clique |
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