The concepts of domination and topological index hold great significance
within the realm of graph theory. Therefore, it is pertinent to merge these
concepts to derive the domination index of a graph. A novel concept of the
domination index is introduced, which utilizes the domination degree of a
vertex. The domination degree of a vertex a is defined as the minimum
cardinality of a minimal dominating set that includes a. The idea of domination
degree and domination index is conducted of graphs like complete graphs,
complete bipartite, r partite graphs, cycles, wheels, paths, book graphs,
windmill graphs, Kragujevac trees. The study is extended to operation in
graphs. Inequalities involving domination degree and already established graph
parameters are discussed. An application of domination degree is discussed in
facility allocation in a city. Algorithm to find a MDS containing a particular
vertex is also discussed in the study