Let $\mathbb{V}$ be a finite dimensional vector space over the field $\mathbb{F}$. $S(\mathbb{V})$ set of all subspaces and $\mathbb{A}\subseteq S^*(\mathbb{V})=S(\mathbb{V})\backslash\{0\}.$ In this paper, we define Cayley subspace sum graph $\mathbb{V},$ denoted by Cay$(S^*(\mathbb{V}),\mathbb{A}), $ as simple undirected with vertex $S^*(\mathbb{V})$ two distinct vertices $X$ $Y$ are adjacent...

We consider the Cayley graph on the symmetric group Sn generated by derangements. It is well known that the eigenvalues of this graph are indexed by partitions of n. We investigate how these eigenvalues are determined by the shape of their corresponding partitions. In particular, we show that the sign of an eigenvalue is the parity of the number of cells below the first row of the corresponding...

Let G be a group and S a subset of G such that the identity element 1 < S and x−1 ∈ S for each x ∈ S . The Cayley graph X(G; S ) on a group G has the elements of G as its vertices and edges joining g and gs for all g ∈ G and s ∈ S . A graph is said to be k-extendable if it contains k independent edges and any k independent edges can be extended to a perfect matching. In this paper, we prove tha...

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...

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...