Abstract
A graph having a vertex-magic total labeling (VMTL) is called vertex-magic. In this paper the existence of VMTLs for several families of rotationally-symmetric graphs, which are generalizations of wheels, is studied. It is shown that the flower F(n) is vertex-magic if and only if n = 3, the generalized s-web graph WB(s)(n, t) is not vertex-magic for n >= 17st + 13s - 1 for any n = qs, s, q >= 2 and the extended Halin graph H(a1,a2, ... , am)(n, t) obtained from the caterpillar S(a1,a2, ... , am) is not vertex-magic for n >= 17mt + 11m + 1 and m >= 1.