Related papers: On the diameter of a super-order-commuting graph
We define a statistic on the graph of commutation classes of a permutation of the symmetric group which is used to show that these graphs are equipped with a ranked poset structure, with a minimum and maximum. This characterization also…
The commuting graph of a group $G$ is the simple undirected graph whose vertices are the non-central elements of $G$ and two distinct vertices are adjacent if and only if they commute. It is conjectured by Jafarzadeh and Iranmanesh that…
Let $X$ be a finite set. We determine the diameter of the commuting graph of the partial transformation semigroup $\mathcal{P}(X)$ on $X$ and show that it coincides with the diameter of the commuting graph of the transformation semigroup…
We construct a family of finite special 2-groups which have commuting graph of increasing diameter
For a division ring D, finite dimensional over its center F, we give a condiction for the connectedness of the commuting graph of a matrix ring over $D$. Furthermore, we prove that if the commuting graph is connected, then its diameter is…
The commuting graph of a finite group with trivial centre is examined. It is shown that the connected components of the commuting graph have diameter at most 10.
We describe the commuting graph of a Rees matrix semigroup over a group and investigate its properties: diameter, clique number, girth, chromatic number and knit degree. The maximum size of a commutative subsemigroup of a Rees matrix…
In this paper, we determine the diameter of the commuting involution graphs of special and general linear groups over an arbitrary field. It turns out that our results also determine the diameter for certain projective special linear groups…
We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the lower bound for the diameter of the commuting graph of the…
In this paper, we study the connectedness of the commuting graph of a general Lie algebra and provide a process to determine whether the commuting graph is connected or not, as well as to compute an upper bound for its diameter. In…
The commuting graph of a semigroup is the set of non-central elements; the edges are defined as pairs $(u,v)$ satisfying $uv=vu$. We provide an example of a field $F$ and an integer $n$ such that the commuting graph of…
Let $G$ be a finite group. Recall that an $A$-group is a group whose Sylow subgroups are all abelian. In this paper, we investigate the upper bound on the diameter of the commuting graph of a solvable $A$-group. Assuming that the commuting…
Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For fixed k, we prove that the diameter of said graph is asymptotically (in q) of order q^(1/k). The same also holds when the generating set…
The commuting graph of a finite soluble group with trivial centre is investigated. It is shown that the diameter of such a graph is at most 8 or the graph is disconnected. Examples of soluble groups with trivial centre and commuting graph…
Integral circulant graphs are proposed as models for quantum spin networks that permit a quantum phenomenon called perfect state transfer. Specifically, it is important to know how far information can potentially be transferred between…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
The commuting graph of a finite non-commutative semigroup $S$, denoted $\cg(S)$, is a simple graph whose vertices are the non-central elements of $S$ and two distinct vertices $x,y$ are adjacent if $xy=yx$. Let $\mi(X)$ be the symmetric…
The orbital diameter of a primitive permutation group is the maximal diameter of its orbital graphs. There has been a lot of interest in bounds for the orbital diameter. In this paper we provide explicit bounds on the diameters of groups of…
The commuting graph of a group G, denoted by Gamma(G), is the simple undirected graph whose vertices are the non-central elements of G and two distinct vertices are adjacent if and only if they commute. Let Z_m be the commutative ring of…
We prove that the diameter of the commuting graph of the full ma- trix ring over the real numbers is at most five. This answers, in the affir- mative, a conjecture proposed by Akbari-Mohammadian-radjavi-Raja, for the special case of the…