Estimation of Graph Parameters Using Graph Convolutional Neural Networks

The paper addresses the potential of deep learning neural network architectures in estimating parameters of a graph. We considered two parameters namely complementary distance pattern uniform (CDPU) number and Kappa. A graph $G =(V, E)$ is a complementary distance pattern uniform (CDPU), if there exists $M\subset V(G)$ such that $f_{M}(u)=\{d(u, v)$: $v\in M\}$, for every $u\in V(G)-M$, is independent of the choice of $u\in V(G)-M$ and the set $M$ is called the CDPU set. The least cardinality of CDPU set in $G$ is called the CDPU number of $G$, denoted by $\sigma(G)$. The vertex connectivity, $\kappa(G)$ of a graph $\mathbf{G}$, is the minimum size of a vertex cut. Graph neural networks are widely used nowadays to solve numerous problems in science, engineering and social domain. Graph convolutinal neural networks (GCN) have been employed to estimate CDPU number and vertex connectivity of a graph. The results show the promise of recent deep learning architectures in estimating parameters of a graph.