On vertex-magic total labeling of some families of rotationally-symmetric graphs

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 ≥ 17si + 13s-1 for any n = qs, s,q ≥2 and the extended Halin graph H _a1 , ,a2,⋯,a_m(n,t) obtained from the caterpillar S_a1,_a2,⋯,a_m is not vertex-magic for n≥ 17mt + 11m + 1 and m≥ 1.