2018/02/20 by Cid-Ruiz, Yairon, Jafari, Sepehr, Nemati, Navid +1
#05C25 #05C38 #05E40 #13D02 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1802.07202
Let I(G) be the edge ideal of a bicyclic graph. In this paper, we characterize the Castelnuovo-Mumford regularity of I(G) in terms of the induced matching number of G. For the base case of this family of graphs, i.e. dumbbell graph, we explicitly compute the induced matching number. Moreover, we prove that reg(I(G)q)=2q+reg(I(G))-2, for all q≥ 1 , when G is a dumbbell graph with a connecting path having no more than two vertices.