We present a logspace algorithm for computing a canonical interval representation and a canonical labeling of interval graphs. As a consequence, the isomorphism and automorphism problems for interval graphs are solvable in logspace.

A simple topological graph T = (V (T), E(T)) is a drawing of a graph in the plane where every two edges have at most one common point (an endpoint or a crossing) and no three edges pass through a single crossing. Topological graphs G and H are isomorphic if H can be obtained from G by a homeomorphism of the sphere, and weakly isomorphic if G and H have the same set of pairs of crossing edges. W...

We consider the complexity of the isomorphism relation on countable first-order structures with transitive automorphism groups. We use the theory of Borel reducibility of equivalence relations to show that the isomorphism problem for vertex-transitive graphs is as complicated as the isomorphism problem for arbitrary graphs, and determine for which first-order languages the isomorphism problem f...

‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.

Graph isomorphism is an important computer science problem. The problem for the general case is unknown to be in polynomial time. The bese algorithm for the general case works in quasi-polynomial time [1]. The solutions in polynomial time for some special type of classes are known. In this work, we have worked with a special type of graphs. We have proposed a method to represent these graphs an...

We introduce an analogue of the bumping algorithm for affine type A, using its natural interpretation in terms of crystals. In fact, we make explicit a particular isomorphism between connected components of the crystal graphs of Fock spaces representations of U q(ŝle). This so-called "canonical" crystal isomorphism turns out to be expressible only in terms of: − Schensted’s bumping procedure, −...

A tournament is a graph in which each pair of distinct vertices is connected by exactly one directed edge. Tournaments are an important graph class, for which isomorphism testing seems to be easier to compute than for the isomorphism problem of general graphs. We show that tournament isomorphism and tournament automorphism is hard under DLOGTIME uniform AC many-one reductions for the complexity...

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...