On the maximal Thurston–Bennequin number of knots and links in spatial graphs

It is known that there does not exist a Legendrian embedding of K4K4 such that all its cycles realize the maximal Thurston–Bennequin numbers that only consist of odd numbers. This paper represents an infinite family of spatial graphs that are Legendrian embeddings of K4K4 such that, for each of the Legendrian embeddings, all its cycles but one realize the maximal Thurston–Bennequin numbers that consist of odd numbers and its one cycle realizes the maximal Thurston–Bennequin number equal to zero.