圖形上有關控制與邊置換成路徑的標號問題之研究

Based on the previous project, we consider the demand for wireless transmission security and accuracy such that the graph formed by a network architecture will allows us to add two directional wireless transmission relay station in each edge of the graph, that is, the edge-path-replacement graph is a graph obtained by replacing each edge of the graph formed by a network architecture with a path having length 3. The known results for L(2,1)-labeling numbers are those graphs with maximum degree less than 3 and upper bounds for others. We have determined the L(2,1)-labeling numbers for those graphs with maximum degree greater than 3 and 3-regular graphs (these reeults will be published on Discrete Mathematics 338(2015) 248-255).