The existence of infinitely many primary trees Original Research Article

As an analogue of the basis elements in a vector space, the primal and primary graphs are studied by Dewdney and other authors. It may be called the binary structure that a tree with diameter ⩽2 is a primary iff it is a star with 2n leaves. This paper further investigates an infinite family of primary trees with binary structures by means of an algorithm related to the matching theory of bipartite graphs.