Nonsymmetric Primitive Translation Schemes on Prime Power Number of Vertices
نویسندگان
چکیده
It is well-known that translation schemes on prime number of vertices are exactly the cyclotomic schemes. In this current paper, we show that there are no nonsymmetric primitive translation schemes on prime square vertices with at most four classes. On the other hand, we find new non-symmetric fourand five-class association schemes from cyclotomy as fission schemes of certain symmetric three-class schemes. Moreover, we provide an affirmative answer to the following question raised by Song [33]: Are there any other two-class primitive schemes that admit symmetrizable fission schemes besides the cyclotomic scheme of index 2 for q ≡ 5 (mod 8)? To be more specific, we show that a certain two-class primitive scheme in the finite field F373 constructed by Feng and Xiang in [11] admits a four-class fission scheme. This fission scheme is realized as a fusion scheme of the cyclotomic scheme of index 28.
منابع مشابه
The Main Eigenvalues of the Undirected Power Graph of a Group
The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...
متن کاملAdjacency metric dimension of the 2-absorbing ideals graph
Let Γ=(V,E) be a graph and W_(a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),… ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...
متن کاملA note on 3-Prime cordial graphs
Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of G if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....
متن کاملComparison of three different numerical schemes for 2D steady incompressible lid-driven cavity flow
In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...
متن کاملNon-symmetric 3-class association schemes
There are 24 feasible parameter sets for a primitive non-symmetric association schemes with 3 classes and at most 100 vertices. Using computer search, we prove non-existence for three feasible parameter sets. Eleven cases are still open. In the imprimitive case, we survey the known results including some constructions of infinite families of schemes. In the smallest case that has been open up t...
متن کامل