Related papers: Graph structure of commuting functions

We investigate the structure of connected graphs, not necessarily locally finite, with infinitely many ends. On the one hand we study end-transitive such graphs and on the other hand we study such graphs with the property that the…

Let $G$ be a $p$-group. We begin to consider the relationship between the structure of the commuting graph and $|G:Z(G)|$. We also build a family of groups whose commuting graphs have more than one connected component whose diameter is at…

The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper we study convex graph invariants, which are graph invariants…

The commuting graph of a group $G$ is the graph whose vertices are the elements of $G$, two distinct vertices joined if they commute. Our purpose in this paper is twofold: we discuss the computational problem of deciding whether a given…

There has been a great deal of attention recently to graphs whose vertex set is a group, defined using the group structure. (The commuting graph, where two elements are joined if they commute, is the oldest and most famous example.) The…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

We explore the relationship between convex and subharmonic functions on discrete sets. Our principal concern is to determine the setting in which a convex function is necessarily subharmonic. We initially consider the primary notions of…

For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…

Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.

In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all…

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…

We consider maps between commutative groups and their functional degrees. These degrees are defined based on a simple idea -- the functional degree should decrease if a discrete derivative is taken. We show that the maps of finite…

We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph…

For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…

In this paper we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node.…

We classify the finite quasisimple groups whose commuting graph is perfect and we give a general structure theorem for finite groups whose commuting graph is perfect.

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

This paper focuses on the discrimination capacity of aggregation functions: these are the permutation invariant functions used by graph neural networks to combine the features of nodes. Realizing that the most powerful aggregation functions…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

In this paper, we consider various graphs, namely: power graph, cyclic graph, enhanced power graph and commuting graph, on a finite semigroup $S$. For an arbitrary pair of these four graphs, we classify finite semigroups such that the…