We consider cellular automata on Cayley graphs and compare their computational powers according to the architecture on which t h e y work. We show that, if there exists a homomorphism with a nite kernel from a group into another one such that the image of the rst group has a nite index in the second one, then every cellular automaton on the Cayley graph of one of these groups can be uni-formall...

In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s ≥ 2. In particular, it is shown that, for any given integer k with k ≥ 3 and k 6= 7, there exists a finite set (maybe empty) of s-transitive Cayley graphs with s ∈ {3, 4, 5, 7} such that all s-transitive Cayley graphs of valency k are their normal covers. This indicates that s-arc transitive Cayley graphs...

Classifying integral graphs is a hard problem that initiated by Harary and Schwenk in 1974. In this paper, with the help of character table, we treat corresponding for Cayley over semi-dihedral group SD8n = ?a,b | a4n b2 1; bab a2n-1?, n ? 2. We present several necessary sufficient conditions integrality SD8n, also obtain some simple terms Boolean algebra hai. particular, give groups SD2n (n?4)...

We prove that the Cayley graphs $X(G,S)$ and $X^+(G,S)$ are equienergetic for any abelian group $G$ symmetric subset $S$. then focus on family of unitary $G_R=X(R,R^*)$, where $R$ is a finite commutative ring with identity. show under mild conditions, $\{G_R, G_R^+\}$ pairs integral non-isospectral (generically connected non-bipartite). Then, we obtain conditions such \bar G_R\}$ graphs. Finall...

Let G be a finite abelian group written additively with identity 0, and Ω an inverse closed generating subset of such that 0 ∉ Ω. We say has the property ‘‘us’’ (unique summation), whenever for every ≠ g ∈ if there are s1, s2, s3, s4 s1 + s2 = s3 s4, then we have {s1, s2} {s3, s4}. Cayley graph Γ Cay(G;Ω) is us-Cayley graph, ‘‘us’’. In this paper, show Aut(Γ) L(G) ⋊ A, where left regular repres...

The spined cube SQn, as a variant network of the hypercube Qn, was proposed in 2011 and has attracted much attention because its smaller diameter. It is well-known that Qn Cayley graph. In present paper, we show SQn an m-Cayley graph, automorphism group semiregular subgroup acting on vertices with m orbits, where m=4 when n≥6 m=⌊n/2⌋ n≤5. Consequently, it shows can be partitioned into eight dis...

We consider the lossless compression of vertex transitive graphs. An undirected graph G = (V, E) is called vertex transitive if for every pair of vertices x, y ∈ V , there is an automorphism σ of G, such that σ(x) = y. A result due to Sabidussi, guarantees that for every vertex transitive graph G there exists a graph mG (m is a positive integer) which is a Cayley graph. We propose as the compre...

In this paper, we introduce a class of double coset cayley digraphs induced by right solvable ward groupoids. These class of graphs can be viewed as a generalization of double coset cayley graphs induced by groups. Further, many graph properties are expressed in terms of algebraic properties.

A Cayley graph Γ = Cay(G, S) is called normal for G, if GR, the right regular representation of G, is a normal subgroup of the full automorphism group Aut(Γ ) of Γ . In this paper we determine the normality of connected and undirected Cayley graphs of valency three for dihedral groups. 2000 Mathematics Subject Classification: 05C25, 20B25.