Edge-neighbor-rupture degree of graphs

The edge-neighbor-rupture degree of a connected graph g is defined to be enrg=maxωg-s-s-mg-s:seg,ωg-s≥1,where s is any edge-cut-strategy of g,ωg-s is the number of the components of g-s,and mg-s is the maximum order of the components of g-s. in this paper,the edge-neighbor-rupture degree of some graphs is obtained and the relations between edge-neighbor-rupture degree and other parameters are determined. © 2013 ersin aslan.