NEW DIRECTION IN THE THEORY OF GRAPH INDEX IN GRAPHS

Since 1972, several graph indices were introduced and studied. In this paper, we define the Banhatti degree of vertex in a graph. We propose the first and second E-Banhatti indices of a graph. A study of E-Banhatti indices in Mathematical Chemistry is a New Direction in the Theory of Graph Index in Graphs. Also we compute these newly defined E-Banhatti indices and their corresponding exponentials for wheel graphs, friendship graphs and some important nanostructures which are appeared in nanoscience.