Abstract:
Guti´errez and Llad´o [19] introduced H-magic labeling of a graph in 2005. Let H and
G(V,E) be simple graphs. A graph G(V,E) admits an H-covering if every edge in
E belongs to a subgraph of G isomorphic to H. A mapping is H-magic if there is a
bijection f : V [E ! {1, 2, . . . , |V | + |E|} such that for each subgraph H0 = (V 0,E0)
of G isomorphic to H, the sum v V 0f(v) + e E0f(e) is constant. If graph G has
a H-magic labeling then graph G is called H-magic graph. If in addition G has the
property that f(V ) = 1, 2, . . . , |V | then G is said to be H-supermagic. In this thesis,
we formulate cycle-supermagic labelings for families of gear graph. We give an answer
to open problem proposed in [1] i.e. we formulate the the C4-supermagic labelings of
generalized gear graphs Gn,s for even n. Further, we formulate all cycle-supermagic
labelings for the generalized gear graph Gn,k, for n 4 and for all values of k 1. At
the end, we give cycle-supermagic labelings of disconnected isomorphic gear graph.
