The Induced Subtree Isomorphism problem takes as input a graph G and a tree T , and the task is to decide whether G has an induced subgraph that is isomorphic to T . This problem is known to be NP-complete on bipartite graphs, but it can be solved in polynomial time when G is a forest. We show that Induced Subtree Isomorphism can be solved in polynomial time when G is an interval graph. In cont...

The d-measurement set of a graph is its set of possible squared edge lengths over all d-dimensional embeddings. In this note, we define a new notion of graph isomorphism called d-measurement isomorphism. Two graphs are d-measurement isomorphic if there is agreement in their d-measurement sets. A natural question to ask is “what can be said about two graphs that are d-measurement isomorphic?” In...

We prove that the Graph Isomorphism problem is fixed-parameter tractable when parameterized by the feedback vertex set number. That parameter is defined as the number of vertex deletions required to obtain a forest. For graphs of bounded feedback vertex set number the presented algorithm runs in time O(n), and is thereby the first fixed-parameter tractable Graph Isomorphism algorithm for a non-...

Given a directed graph, there exists a universal operator algebra and universal C-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C-algebra of an operator algebra. We also discuss uniqueness of the universal algebras for finite graphs, showing that for finite graphs the graph is an isom...

Graphs are widely used to model complicated data semantics in many applications. In our paper [8], we proposed Fast-ON, an efficient algorithm for subgraph isomorphism problem. In this paper, we develop an efficient algorithm called Fast-ON* that extends Fast-ON to handle two other problems, namely, graph isomorphism problem and graph query processing. Our performance study shows that Fast-ON* ...

The questions of isomorphism degree estimation of fuzzy graphs are discussed in this paper. The definition of independent fuzzy set of fuzzy graph is presented. The estimation method of isomorphism degree of fuzzy graphs is suggested and proved. The example of isomorphism degree estimation is considered.

We study the isomorphism problem of two “natural” algebraic structures – F-algebras and cubic forms. We prove that the F-algebra isomorphism problem reduces in polynomial time to the cubic forms equivalence problem. This answers a question asked in [AS05]. For finite fields of the form 3 6 |(#F − 1), this result implies that the two problems are infact equivalent. This result also has the follo...

In this paper we examine the hard problems underlying asymmetric pairings, their precise relationships and how they affect a number of existing protocols. Furthermore, we present a new model for the elliptic curve groups used in asymmetric pairings, which allows both an efficient pairing and an efficiently computable isomorphism.

In this paper an improved version of a graph matching algorithm is presented, which is able to efficiently solve the graph isomorphism and graph-subgraph isomorphism problems on Attributed Relational Graphs. This version is particularly suited to work with very large graphs, since its memory requirements are quite smaller than those of other algorithms of the same kind. After a detailed descrip...

Enumerating the isomorphism classes of several types of graph coverings is one of the central research topics in enumerative topological graph theory (see [R. Feng, J.H. Kwak, J. Kim, J. Lee, Isomorphism classes of concrete graph coverings, SIAM J. Discrete Math. 11 (1998) 265–272; R. Feng, J.H. Kwak, Typical circulant double coverings of a circulant graph, Discrete Math. 277 (2004) 73–85; R. F...