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An Algorithmic-type Classification of Tetravalent One-regular Graphs Using Computer Algebra Tools

Ghasemi M.

Fundamenta Informaticae

2014

Vol. 135, nr 3

211--228

A finite graph is one-regular if its automorphism group acts regularly on the set of its arcs. In the present paper, tetravalent one-regular graphs of order 7p2., where p is a prime, are classified using computer algebra tools.

A note introducing Cayley graphs and group-coset graphs generated by graph packings

Rosiek R., Woźniak M.

Opuscula Mathematica

2004

Vol. 24, no. 2

203-221

The aim of this paper is to construct a class of vertex-transitive graphs that includes the Kneser graphs as a special case. The class will be based on the notion of packing of graphs. Certain families of graphs within this class will be examined more closely, and some of their properties, such as hamiltonicity, will be investigated.

Effective Simulations on Hyperbolic Networks

Nichitiu C.M., Rémila E.

Fundamenta Informaticae

2002

Vol. 52, nr 1-3

203-231

We state a definition of the simulation of graph automata, which are machines built by putting copies of the same finite-state automaton at the vertices of a regular graph, reading the states of the neighbors. We first present the notion of simulation and link it to intrinsic graph properties. Afterwards, we present some results of simulation between such graph automata, comparing them to the cellular automata on Cayley graphs. The graphs considered here are planar, with the elementary cycles of the same length, and form regular tilings of the hyperbolic plane. We conclude with a possible speed hierarchy.