Very Well-Covered Graphs via the Rees Algebra
摘要
A very well-covered graph is a well-covered graph without isolated vertices such that the size of its minimal vertex covers is half of the number of vertices. If G is a Cohen–Macaulay very well-covered graph, we deeply investigate some algebraic properties of the cover ideal of G via the Rees algebra associated to the ideal, and especially when G is a whisker graph.