An Introduction to Nano Ideal Graph of a Graph

Abstract

Nano ideal graph of a simple , undirected graph G is introduced. As the size of the Nano ideal graph of a graph G is smaller than the graph G, we attempt to approach some of the properties like isomorphism between two graphs, connectedness and coloring properties of graphs via Nano ideal graph of the graph G. A typical u-v path of the graph G becomes an uv edge in Nano ideal graph of a graph, analysis of isomorphism between trees become simple when using Nano ideal graphs