Volume 35 • Number 1 • 2012   • The Edge Steiner Number of a Graph Michael B. Frondoza and Sergio R. Canoy, Jr. Abstract. The concepts of edge Steiner set and edge Steiner number of a graph are investigated in this study. A necessary and sufficient condition for a graph $G$ to satisfy ${\rm st}_e(G) = \vert V(G) \vert - 1$, where ${\rm st}_e(G)$ denotes the edge Steiner number of $G$, is obtained. Edge Steiner sets in the joins of graphs are also studied and the Steiner numbers of these graphs are determined. 2010 Mathematics Subject Classification: 05C12. Full text: PDF