設G為一無向圖，若在G的每一邊上指定非零整數，使得在每一頂點之所有鄰接邊的整數和為零，稱此圖形G具有零和流(Zero-sum flow)。若邊上之指定整數均來自集合{±1,±2, ...,±(k− 1)}，則稱其為一零和k-流(Zero-sum k-flow)。進一步可定義圖G之零和流數(Zero-sum flow number)，使得G具有零和k-流之最小值k。本論文主要探討河內圖形以及相關的(2, 3)-圖形之零和流與零和流數，並且提出未來可繼續努力的方向。 For an undirected graph G, let E(v) denote the set of edges incident on a vertex v ∈ V(G). A zero-sum flow is an assignment of non-zero integers to the edges such that the sum of the values v of all edges incident with each vertex is zero.A zero-sum k-flow is a zero-sum flow whose values are integers with absolute value less than k.This paper study on zero-sum flow numbers of hanoi graphs and related (2,3)-Graphs. Open problems are listed in the last section.
