In this paper, we propose a formalization of the features that a graph representation of logic programs under the answer set semantics should in our opinion exhibit in order to be a satisfactory and useful representation formalism. We introduce a concept of isomorphism between a program and the corresponding graph. We show the importance of isomorphism for program analysis and we compare differ...

Kwak, J.H. and J. Lee, Isomorphism classes of cycle permutation graphs, Discrete Mathematics 105 (1992) 131-142. In this paper, we construct a cycle permutation graph as a covering graph over the dumbbell graph, and give a new characterization of when two given cycle permutation graphs are isomorphic by a positive or a negative natural isomorphism. Also, we count the isomorphism classes of cycl...

Graph theory has an important role in the area of applications of networks and clustering‎. ‎In the case of dealing with uncertain data‎, ‎we must utilize ambiguous data such as fuzzy value‎, ‎fuzzy interval value or values of fuzzy number‎. ‎In this study‎, ‎values of fuzzy number were used‎. ‎Initially‎, ‎we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value f...

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...

The problem of determining whether two given finite graphs are isomorphic is easily seen to belong to the class NP. But up to now, no polynomial time algorithm is known. On the other hand, no NP-completeness proof is known either. That is, GRAPH ISOMORPHISM is one of the few “open problems” in NP according to Garey and Johnson’s terminology [9]. Note that GRAPH ISOMORPHISM is already mentioned ...

We show that the graph isomorphism problem is hard under logarithmic space many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space), for every logarithmic space modular class ModkL and for the class DET of problems NC1 reducible to the determinant. These are the strongest existing hardness results for the graph isomorphism problem, and imply a randomized logarithm...

We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c ≥ 1 of deletion: 1. GI ≡iso VDCc, GI ≡iso EDCc, GI ≤m LVDc, and GI ≡iso LEDc. 2...

We propose a new approach to solve graph isomorphism using parameterized matching. To find isomorphism between two graphs, one graph is linearized, i.e., represented as a graph walk that covers all nodes and edges such that each element is represented by a parameter. Next, we match the graph linearization on the second graph, searching for a bijective function that maps each element of the firs...

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability graphs of partially ordered sets with interval dimension 2 and height 3. In contrast, the problem is known to be solvable in polynomial time for comparabilit...