Invariants of spatial graphs coming from maximal trees

Abstract

In this paper, we find that for each given spatial graph, the number of its maximal trees is finite, and the quotient space corresponding to some maximal tree is also a spatial graph and it is homeomorphic to a disjoint union of wedge sum of circles. That means this quotient space is orientable and colorable. Thus, we define two equivalence invariants of spatial graphs, the coloring number bracket and the Alexander invariant set, which are coming from the coloring invariant and Alexander matrix.