Zero-Sum Flow Numbers of (2,3)-Graphs

• Main Authors: Eu, Zhen-Kui, 游鎮魁
• Other Authors: Weng, Chih-Wen
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/52341776784625336317

碩士 === 國立交通大學 === 應用數學系所 === 104 === 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 f of non-zero real numbers on the edges of G such that ∑ f (e) = 0 e∈E(v) for all v ∈ V(G). A zero-sum k-flow is a zero-sum flow with integers from the set {±1,...,±(k−1)}. Let zero-sum flow number F(G) be defined as the least number of k such that G admits a zero-sum k-flow. In this paper, a necessary and sufficient condition for (2,3)-graph G with F(G) = 3 is given. Furthermore we study zero-sum flow number of (2,3)-graphs expanded from path and tree, namely, the Christmas lamps, the tree lamps, respectively, and conclude that their zero-sum flow numbers are at most 5.