Most notably , the parameters called connectivity and line - connectivity have been frequently used . the connectivity of a graph g is the least number of vertices of g whose removal disconnects g similarly , the line - connectivity of g is the least number of g whose removal disconnects g the higher the connectivity ( edge - connectivity ) of g , the more stable it is considered to be 而這些研究工作主要是圍繞點(diǎn)連通度,邊連通度,局部點(diǎn)、邊連通度來做的,但隨著圖的連通性研究的不斷深入,人們越來越覺得僅用點(diǎn)連通度,邊連通度,局部點(diǎn)、邊連通度來描述圖的連通性存在很大的局限性。
For the two sides above , it is urgent for us to find new parameters to measure the stability of graphs . consequently , a number of other parameters have recently been introduced in an attempt to cope with the difficulty which the connectivity and line - connectivity have , including toughness , edge - toughness , tenacity , edge - tenacity , scattering number and integrity 正因如此,在圖的連通性研究中,迫切需要一個(gè)既能反映系統(tǒng)被破壞的難易程度又能反映系統(tǒng)遭受破壞程度的參數(shù),而圖的完整度正是符合這樣要求的一個(gè)參數(shù)。