Influence of Krylov subspace in Graph Isomorphism for Mobile Networks

Abstract

Identification of isomorphism among graphs is one of the computationally challenging tasks in computer science that couldn’t be solved in polynomial time. In this paper, we derive a polynomial time algorithm that allows direct comparison between different graph structures to check for graph isomorphism. This paper suggest to represent graphs in a common mathematical space (Symmetric Positive Semi-Definite space), so that two isomorphic graphs always map to the same coordinates in a mathematical space. This kind of mathematical representation is generated based on the neighbourhood influences between nodes of a graph which enhances the graph topological structure at the node level in the form of krylov subspace, in polynomial time. Experiments are conducted using publicly available benchmark graph database. From the simulation, it is observed that the representation recommended in this work acts like a signature for each graph with guaranteed isomorphism. Further the proposed approach tries to identify the molecular structure of any application-specific graphs and categorizes them effectively in a polynomial time inspite of its NP-completeness.