In this paper, we will determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this will complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we deter...

In this paper, we introduce the notion of N -graphs and describe methods of their construction. We prove that the isomorphism between N -graphs is an equivalence relation (resp. partial order relation). We then introduce the concept of N -line graphs and discuss some of their fundamental properties.

A rainbow graph is a graph that admits a vertex-coloring such that every color appears exactly once in the neighborhood of each vertex. We investigate some properties of rainbow graphs. In particular, we show that there is a bijection between the isomorphism classes of n-rainbow graphs on 2n vertices and the switching classes of graphs on n vertices.

The question of whether there is a polynomial time algorithm deciding whether two graphs are isomorphic has been a one of the best known open problems in theoretical computer science for more than forty years. Indeed, the graph isomorphism problem is one of the very few natural problems in NP that is neither known to be in P nor known to be NP-complete. The question is still wide open, but a nu...

We relate the graph isomorphism problem to the solvability of certain systems of linear equations and linear inequalities. The number of these equations and inequalities is related to the complexity of the graphs isomorphism and subgraph isomorphim problems. 2000 Mathematics Subject Classification: 03D15, 05C50, 05C60, 15A48, 15A51, 15A69, 90C05.

The isomorphism problem for Cayley graphs over a group H will be considered and solved completely for cyclic groups H of prime power order for every prime p including p = 2. The method we use to obtain our solution is based on Schur rings. This method can be applied as well to colored Cayley graphs, and its scope admits further generalizations. 1. How to solve the isomorphism problem? In this p...

We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their sub-triangles. In the second part, we propose graph representations in terms of one-dimensional distributions (e.g., distribution of the node weights, sum of ...

Given a function f in a finite field IFq we define the functional graph of f as a directed graph on q nodes labelled by elements of IFq where there is an edge from u to v if and only if f(u) = v. We obtain some theoretic estimates on the number of non-isomorphic graphs generated by all polynomials of a given degree. We then develop an algorithm to test the isomorphism of quadratic polynomials t...

Several graph problems (e.g., steiner tree, connected domination, hamiltonian path, and isomorphismproblem), which can be solved in polynomialtime for distance-hereditary graphs, are NP-complete or open for parity graphs. Moreover, the metric characterizations of these two graph classes suggest an excessive gap between them. We introduce a family of classes forming an innnite lattice with respe...

Graph matching or quadratic assignment, is the problem of labeling the vertices of two graphs so that they are as similar as possible. A common method for approximately solving the NP-hard graph matching problem is relaxing it to a convex optimization problem over the set of doubly stochastic matrices. Recent analysis has shown that for almost all pairs of isomorphic and asymmetric graphs, the ...