computers and the connections between them in single domainlike wiley comform subgraph of the internet if this subgraph is connectedthen two users on computers in this domain can send -mail to one another without having their information packets ever leave their domain suppose the edges of this subgraph form spanning tree this implies thatif even single connection goes down (for examplebecause someone pulls communication cable out of the back of computer in this domain)then this subgraph will no longer be connected there are number of simple properties of treesforestsand connected graphs proposition let be an undirected graph with vertices and edges if is connectedthen >= if is treethen if is forestthen <= we leave the justification of this proposition as an exercise ( - the graph adt as an abstract data typea graph is collection of elements that are stored at the graph' positions--its vertices and edges hencewe can store elements in graph at either its edges or its vertices (or bothin javathis means we can define vertex and edge interfaces that each extend the position interface let us then introduce the following simplified graph adtwhich is suitable for vertex and edge positions in undirected graphsthat isgraphs whose edges are all undirected additional methods for dealing with directed edges are discussed in section vertices()return an iterable collection of all the vertices of the graph edges()return an iterable collection of all the edges of the graph incidentedges( )return an iterable collection of the edges incident upon vertex opposite( , )return the endvertex of edge distinct from vertex van error occurs if is not incident on