Several theoretical results are obtained by studying symmetric Eulerian graph and symmetric Eulerian trail .

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The study of symmetric graphs is an active area in graph theory .

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Because only the triangle matrix information is encoded in the symmetric matrix that describes all possible changes of the undirected network the length of coding string is moderate and there is no limitation of edges for modeling the whole evolution from the tree to complete graph .

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Let DKv denote the symmetric complete directed graph with v vertices the covering number C ( v m ) is a minimum number of covering DKv by m-circuits .

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