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  • Title
  • Certificate
  • Declaration
  • Acknowledgement
  • Contents
  • Preface
  • 1. Preliminaries
  • 1.2 Basic graph theory
  • 1.3 Domination in graphs
  • 1.4 Metric dimension of graphs
  • 1.5 Fractional graph theory
  • 2. Fractional distance domination in graphs
  • 2.2 Minimal k-dominating functions
  • 2.3 Graphs with γkf (G) = γk(G)
  • 2.4 Convexity of k-dominating functions
  • 3. Fractional Y-domination in bipartite graphs
  • 3.2 Minimal Y -dominating functions
  • 3.3 Convexity of Y -dominating functions
  • 3.4 Computational complexity of Y f (G)
  • 4. Fractional metric dimension of graphs
  • 4.2 Resolving functions of a graph
  • 4.3 Graphs with dimf (G) = |V (G)|
  • 4.4 Fractional metric dimension of some standard graphs
  • 4.5 Graphs with dimf (G) = dim(G)
  • 4.6 Fractional metric dimension of Cartesian product of graphs
  • 5. Minimal resolving functions in graphs
  • 5.2 Convexity of minimal resolving functions
  • 5.3 Universal minimal resolving functions
  • 5.4 Resolving convexity graph
  • Bibliography