Resolving Topological Indices of Graphs

Topological indices are graph invariants most suitable for underlined structures of chemical compounds. Most of the topological indices are defined on the well-known graph concepts such as degree of a vertex, distances, eccentricity of a vertex etc. In this paper, new type of degree of a vertex is defined with the aid of resolving property of the graph as the minimum cardinality of a resolving set containing that vertex. The mathematical properties of this newly defined degree is established with the help of standard graphs and an attempt to analyze its applicability in chemical compounds are carried by taking silicate structures.