Abstract
This paper proposes an approach based on graph isomorphism to find the correspondence in relational matching. We describe a pseudo-automorphism group as Pseudo-aut (G) of a graph G, which is a set of all pseudo-automorphisms of G. We discuss some properties of the Pseudo-aut(C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) and the relationships between various elements, establish the relationship between the pseudo-isomorphic and the perfect matching. From these we reach some important conclusions: the Petersen graph is a special element of the Pseudo-aut(C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sub> ); the composition of the Petersen graph is just one of its origins; there exists a Hamiltonian graph of order 12, which is 3-connected, 3-regular, non-planar, non-bipartite, and its girth is 5.
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