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For every undirected graph, Tutte [3] defined a polynomial TG(x;y) in two variables which plays an important role in graph theory.Now this polynomial is called Tutte polynomial.It contains information about how the graph is connected.For example, TG(1;1) is the number of spanning trees in G, TG(2;1) is the number of spanning forests in G.As universality of graph language, Tutte polynomial contains several famous other specialisations from other sciences such as the Jones polynomial from knot theory and the partition functions of the Potts model from statistical physics.