The fixed-parameter tractability of graph isomorphism is an open problem with respect to a number of natural parameters, such as tree-width, genus and maximum degree. We show that graph isomorphism is fixed-parameter tractable when parameterized by the tree-depth of the graph. We also extend this result to a parameter generalizing both tree-depth and max-leaf-number by deploying new variants of...

Graphs are powerful data structure to represent objects and their concepts. Objects are nothing but nodes and edges describes relation among objects. Number of real world problems is represented by graph. Graph isomorphism is the area of pattern matching and widely used in various applications such as image processing, protein structure, computer and information system, chemical bond structure,...

A new approach of graph matching is introduced in this paper, which efficiently solves the problem of graph isomorphism and subgraph isomorphism. In this paper we are introducing a new approach called SubGraD, for query graph detection in source graph. Firstly consider the model graph (query graph) and make the possible sets called model sets starting from the chosen initial node or starter. Si...

We consider the PermCode problem to decide, given a representation of a permutation group G and a parameter k, whether there is a non-trivial element of G with support at most k. This problem generalizes several problems in the literature. We introduce a new method that allows to reduce the maximal orbit size of the group being considered while maintaining elements with small support in the gro...

We present a novel randomized approach to the graph isomorphism problem. Our algorithm aims at solving difficult instances by producing randomized certificates for non-isomorphism. We compare our implementation to the de facto standard nauty. On many of the hardest known instances, the incidence graphs of finite projective planes, our program is considerably faster than nauty. However, it is in...

The graph isomorphism problem consists in deciding whether two given graphs are isomorphic and thus, consists of determining whether there exists a bijective mapping from the vertices of one graph to the vertices of the second graph such that the edge adjacencies are respected. The graph isomorphism problem is a well-known open problem that was first listed as an important open problem by Karp,...

We propose a novel variational method for solving the sub-graph isomorphism problem on gate-based quantum computer. The relies (1) new representation of adjacency matrices underlying graphs, which requires number qubits that scales logarithmically with vertices graphs; and (2) ansatz can efficiently probe permutation space. Simulations are then presented to showcase approach graphs up 16 vertic...