In this paper, we generalize the regular graph of R to the M-regular graph of R, denoted by M-Reg(Γ(R)). It is the undirected graph with all M-regular elements of R as vertices, and two distinct vertices x and y are adjacent if and only if x+y ∈ Z(M). The basic ...
The b-chromatic number of a graph G, denoted by φ(G), is the largest integer k such that G has a proper vertex coloring with k colors in which each color class contains a vertex that is adjacent to at least one vertex in each of the other color classes. El Sahili and Kouider aske...
A quasi-strongly regular graph with parameters(n,k,a;c1,c2,…,cp), denoted by QSRG(n,k,a;c1,c2,…,cp), is ak-regular graph onnvertices such that any two adjacent vertices haveacommon neighbours and any two non-adjacent vertices havecicommon neighbours for some1≤i≤p, wherea,c1,c...
Let G be astrong regular graph(denoted by srg in short) with parameters(n,k,λ,μ). 设G是一个具有参数(n,k,λ,μ)的强正则图,首先讨论了图G的一些性质以及参数n,k,λ和μ之间的关系,特别地,提出了一个关于参数n,k,λ和μ的整性条件。
强正则图 1. Let G be a strong regular graph(denoted by srg in short) with parameters(n,k,λ,μ). 设G是一个具有参数(n,k,λ,μ)的强正则图,首先讨论了图G的一些性质以及参数n,k,λ和μ之间的关系,特别地,提出了一个关于参数n,k,λ和μ的整性条件。6) s-regular graphs s-正则图补充...
TheFrattini subgroupof a finite groupG, denoted by\(\Phi (G)\), is defined to be the intersection of all maximal subgroups ofG, and\(\Phi (G)\)can be characterized as the set of non-generators ofG. Proposition 2.4 [13, Theorem 9.2(a)] LetGbe a finite group and\(S \subset G\...
The recoloring framework consists in finding step-by-step transformations between two proper colorings such that all intermediate states are also proper. More formally, two k-colorings are adjacent if they differ on exactly one vertex. The k-recoloring graph of G, denoted by Ck(G) and defined...
In network theory, the connectivity of a graph G, denoted by κ(G), is an integer number, such that at least κ(G) nodes have to be removed to disconnect G. κ(G) is closely related to the reliability and fault tolerability of the network G. It is, however, limited by the ...
Given the relation between the weights of a projective three-weight code and the eigenvalues of the coset graph of its dual, corresponding solutions of Eq. (1) can be easily enumerated. However, not all cases are feasible, i.e., attainable by a projective three-weight code. The aim of ...
An instance of this problem (which will be denoted by 1-in-3SAT) consists of a set X of boolean variables and a collection C={c1,…,cm} of m clauses over X, such that each ci has |ci|=3 and does not contain any negated literal. One-in-3SAT asks whether there is a truth ...