Trofimov, V. I.
Published in
Proceedings of the Steklov Institute of Mathematics

Using a simple but rather general method of constructing Cayley graphs with trivial vertex stabilizers, we give an example of an infinite locally finite Cayley graph (and, hence, an example of an infinite connected locally finite vertex-symmetric unimodular graph) which is isolated in the space of connected locally finite vertex-symmetric graphs. W...

Caucal, Didier

We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.

Caucal, Didier

We present simple graph-theoretic characterizations for the Cayley graphs of monoids, right-cancellative monoids, left-cancellative monoids, and groups.

cheng, tao feng, lihua liu, weijun

We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group M 4 n = &lang / a , b | a n = b 4 = 1 , b &minus / 1 a b = a &minus / 1 &rang / , some of which generalize those earlier constructions. For a prime p and a positive integer &alpha / > / 1 , for some cases, we characterize the DSRCGs ove...

Ashrafi, A Bretto, Alain Gholaminezhad, F

Let G be a finite group and Φ(G, S) is the G−graph of a group G with respect to a non-empty subset S. The aim of this paper is to study the structure and the automorphism group of a simple form of G−graph for some finite groups like alternating group, dihedral, semi-dihedral, dicyclic, Zm δ Z2n, where δ is inverse mapping and V8n = {a, b|a 2n = b 4...

Stewart, Ian

In 1957 Steinhaus asked for a proof that a chain of identical regular tetrahedra joined face to face cannot be closed. ´Swierczkowski gave a proof in 1959. Several other proofs are known, based on showing that the four reﬂections in planes though the origin parallel to the faces of the tetrahedron generate a group R isomorphic to the free product Z...

Gao, Yipeng Wang, Yunzhi Zhang, Yongfeng
Published in
IUCrJ

The generation and motion of crystalline defects during plastic deformation are critical processes that determine the mechanical properties of a crystal. The types of defect generated are not only related to the symmetry of a crystal but also associated with the symmetry-breaking process during deformation. Proposed here is a new mathematical frame...

Petek, Ana

V magistrskemu delu se ukvarjamo z znano družino precej simetričnih grafov. To so tako imenovani Cayleyjevi grafi. V zvezi z njimi je zanimivo vprašanje o obstoju hamiltonskih poti oziroma hamiltonskih ciklov v takšnih grafih. Cayleyjevi grafi so grafi, katerih vozlišča so elementi dane grupe, povezave pa so dane s pomočjo tako imenovane povezavne ...

Dai, Wenjing Yuan, Jiabin Li, Dan
Published in
Quantum Information Processing

The finite dihedral group generated by one rotation and one flip is the simplest case of the non-Abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the dihedral group. Considering the characteristics of the elements in the dihedral group, we conduct the model of discre...

Mufti, Z Nadeem, M Ahmad, Ali Ahmad, Z

Let G = (V, E) be a connected graph, let x ∈ V (G) be a vertex and e = yz ∈ E(G) be an edge. The distance between the vertex x and the edge e is given by d G (x, e) = min{d G (x, y), d G (x, z)}. A vertex t ∈ V (G) distinguishes two edges e, f ∈ E(G) if d G (t, e) = d G (t, f). A set R ⊆ V (G) is an edge metric generator for G if every two edges of...