In this paper, we give formulas for v-number of edge ideals of some graphs
like path, cycle, 1-clique sum of a path and a cycle, 1-clique sum of two
cycles and join of two graphs. For an m-primary monomial ideal
IβS=K[x1β,β¦,xtβ], we provide an explicit expression of v-number
of I, denoted by v(I), and give an upper bound of v(I) in terms of the
degree of its generators. We show that for a monomial ideal I, v(In+1)
is bounded above by a linear polynomial for large n and for certain classes
of monomial ideals, the upper bound is achieved for all nβ₯1. For
m-primary monomial ideal I we prove that v(I)β€ reg(S/I)
and their difference can be arbitrarily large.Comment: 15 page