A subclass of the class of circulant graphs is considered. It is shown that in this subclass, isomorphism is equivalent to Adam-isomorphism. Various results are obtained for the chromatic number, line-transitivity and the diameter.

We give explicit and efficiently computable formulas for the number of isomorphism classes of I-graphs, connected I-graphs, and generalized Petersen graphs. The tool that we use is the well-known Cauchy-FrobeniusBurnside lemma.

Algorithms testing two graphs for isomorphism known as yet in computer science have exponential worst case complexity. In this paper we propose an algorithm that has polynomial complexity and constructively supplies the evidence that the graph isomorphism lies in P.

Graph isomorphism problem is to determine whether two given graphs are isomorphic. It is a particular type of a more general problem “the isomorphism of incidence system”. I propose some new invariants for heuristic search of graph isomorphism and demonstrate that they are really useful in practice by experiments. Keyword. graph isomorphism, graph invariant, graph spectrum , adjacency matrix, m...

We investigate spectra of Cayley graphs for the Heisenberg group over finite rings Z/pnZ, where p is a prime. Emphasis is on graphs of degree four. We show that for odd p there is only one such connected graph up to isomorphism. When p = 2, there are at most two isomorphism classes. We study the spectra using representations of the Heisenberg group. This allows us to produce histograms and butt...

We investigate spectra of Cayley graphs for the Heisenberg group over Þnite rings Z/pZ, where p is a prime. Emphasis is on graphs of degree four. We show that for odd p there is only one such connected graph up to isomorphism. When p = 2, there are at most two isomorphism classes. We study the spectra using representations of the Heisenberg group. This allows us to produce histograms and butter...

We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish no...

We show that the problem to decide whether two (convex) polytopes are combinatorially isomorphic is graph isomorphism complete, even for simple or simplicial polytopes. On the other hand, we give a polynomial time algorithm for the polytope isomorphism problem in bounded dimension, which is based on Luks’ algorithm for the isomorphism problem of graphs of bounded maximal degree.