  In this paper, we study the graph isomorphism and graph automorphism
problems. We propose a novel technique to analyze graph isomorphism and graph
automorphism. Further we handled some strongly regular datasets for prove the
efficiency of our technique. The neighbourhood matrix $ \mathcal{NM}(G) $ was
proposed in \cite {ALPaper} as a novel representation of graphs and was defined
using the neighbourhood sets of the vertices. It was also shown that the matrix
exhibits a bijection between the product of two well known graph matrices,
namely the adjacency matrix and the Laplacian matrix. Further, in a recent
work\cite{NM_SPath}, we introduced the sequence of matrices representing the
powers of $\mathcal{NM}(G)$ and denoted it as $ \mathcal{NM}^{\{l\}}, 1\leq l
\leq k(G)$ where $ k(G) $ is called the \textbf{iteration number},
$k(G)=\ceil*{\log_{2}diameter(G)} $. In this article we introduce a structural
descriptor given by a sequence and clique sequence for any undirected
unweighted simple graphs with help of the sequences of matrices $ NM^{\{l\}} $.
The $ i^{th} $ element of structural descriptor sequence encodes the complete
structural information of the graph from the vertex $ i\in V(G) $. The $ i^{th}
$ element of clique sequence encodes the Maximal cliques on $ i $ vertices. The
above sequences is shown to be a graph invariants and is used to study the
graph isomorphism and automorphism problem.
