Two-dimensional cycle classes on $$\overline{\mathcal {M}}_{0,n}$$

On two-dimensional Cayley graphs

A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....

On Pre-θ-Open Sets and Two Classes of Functions

Some numerical results on two classes of finite groups

In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...

On two equimatchable graph classes

A graph G is said to be equimatchable if every matching in G extends to (i.e., is a subset of) a maximum matching. In this paper, we use the Gallai–Edmonds decomposition theory for matchings to determine the equimatchable members of two important graph classes. We 5nd that there are precisely 23 3-connected planar graphs (i.e., 3-polytopes) which are equimatchable and that there are only two cu...

Complexity Classes in the Two-dimensional Life Cellular Automata Subspace

Cellular automata (CA) are a class of discrete dynamical models which represent an approximation to physical systems composed of a large number of simple and locally interacting elements [18]. They have caught the interest of many researchers because of their rich and diverse phenomenology [16]. In this framework, Wolfram has shown that CA exhibit the full spectrum of dynamical behaviors [19] a...