Aslan, E2025-04-102025-04-100129-0541http://hdl.handle.net/20.500.14701/34474The rupture degree of a graph is a measure of the vulnerability of a graph. In this paper we investigate a refinement, that involves the weak version of the parameter. The weak rupture degree of a connected graph G is defined to be R-w(G) = max{w(G - S) - |S| - m(e)(G - S) : S subset of V (G), w (G - S) > 1} where w(G - S) is the number of the components of G - S and m(e)(G - S) is the number of edges of the largest component of G - S. Like the rupture degree itself, this is a measure of the vulnerability of a graph, but it is more sensitive. This paper, the weak-rupture degree of some special graphs are obtained and sonic bounds of the weak-rupture degree are given. Moreover some results about the weak-rupture degree of graphs obtained by graph operations are given.EnglishArticle1793-6373