chapter  2
Trees and Connectivity
Pages 52

In nearly every concept, problem and theorem that we encounter, we are primarily concerned with connected graphs. There are various ways of measuring connectedness for graphs and in many instances, it will be important for us to know the degree of connectedness of the graphs being considered. While a graph may contain a u− v path for every pair u, v of vertices and consequently is connected, a graph can satisfy this requirement in minimal ways or in much stronger ways.