Publication Type: Conference Paper/Unpublished Manuscript
Abstract: The distance from a vertex u to a vertex v in a connected graph G is the length of a shortest u–v path in G. The eccentricity of a vertex v in a connected graph is the distance between v and a vertex farthest from v. The center of a graph is the subgraph induced by those vertices having minimum eccentricity while the periphery is the subgraph induced by those vertices having maximum eccentricity. The distance of a vertex v in G is the sum of the distances from v to the vertices of G. The median of a graph is the subgraph induced by those vertices having minimum distance. Other distance related subgraphs will also be defined during this talk. Graph theory problems related to these subgraphs are excellent for undergraduate research projects. For example, we could consider the relative location of subgraphs or the appendage number of a subgraph. We also investigate what happens when an edge is removed from the graph at random.