We call a finite simple graph G = (V (G),E(G)) to be Z-semimagic if it admits an edge labeling l : E(G) ¡÷ Z {0} such that the induced vertex sum labeling l+(v) = uv∈E(G) l(uv) is constant. The constant is called a semimagic index, or an index for short, of G under the labeling l. We consider the set of all possible semimagic indices r such that G is Z-semimagic with a semimagic index r, and denote it by IZ(G). We call IZ(G) the index set of G with respect to Z. In this thesis, we decide the index set IZ(G) for G being regular graphs, complete bipartite graphs, wheel graphs and fan graphs. Also, we determine whether 0 ∈ IZ(G) for G being complete multi-partite graphs.

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"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling." / Doctor of Philosophy

"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling." / Doctor of Philosophy