相关论文: On some automorphism related parameters in graphs

The fractional versions of graph theoretic-invariants multiply the range of applications in scheduling, assignment and operational research problems. In this paper, we introduce the fractional version of local metric dimension of graphs.…

In this paper, we consider the probability that a randomly chosen automorphism of a finite group fixes a randomly chosen element of a subgroup of that group. We obtain several new results as well as generalizations and improvements of some…

The purpose of this note is to define a graph whose vertex set is a finite group $G$, whose edge set is contained in that of the commuting graph of $G$ and contains the enhanced power graph of $G$. We call this graph the deep commuting…

Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…

Graphs are a useful abstraction of image content. Not only can graphs represent details about individual objects in a scene but they can capture the interactions between pairs of objects. We present a method for training a convolutional…

In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ on graphs. Towards this, we proposed the concepts of class obstruction,…

The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact…

Let $G$ be a group. The directed endomorphism graph, \dend of $G$ is a directed graph with vertex set $G$ and there is a directed edge from the vertex `$a$' to the vertex `$\, b$' $(a \neq b) $ if and only if there exists an endomorphism on…

There has been substantial interest in estimating the value of a graph parameter, i.e., of a real-valued function defined on the set of finite graphs, by querying a randomly sampled substructure whose size is independent of the size of the…

Consider the setting of \emph{randomly weighted graphs}, namely, graphs whose edge weights are chosen independently according to probability distributions with finite support over the non-negative reals. Under this setting, properties of…

An important facet of the inverse eigenvalue problem for graphs is to determine the minimum number of distinct eigenvalues of a particular graph. We resolve this question for the join of a connected graph with a path. We then focus on…

A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…

When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we…

Structural features are important features in a geometrical graph. Although there are some correlation analysis of features based on covariance, there is no relevant research on structural feature correlation analysis with graph neural…

The \emph{metric dimension} of a graph $G$, denoted by $\dim(G)$, is the minimum number of vertices such that each vertex is uniquely determined by its distances to the chosen vertices. Let $G_1$ and $G_2$ be disjoint copies of a graph $G$…

The functionality of a graph $G$ is the minimum number $k$ such that in every induced subgraph of $G$ there exists a vertex whose neighbourhood is uniquely determined by the neighborhoods of at most $k$ other vertices in the subgraph. The…

Inspired by notorious combinatorial optimization problems on graphs, in this paper we consider a series of related problems defined using a metric space and topology determined by a graph. Particularly, we present the Independent Set,…

We present in this article the model Function-described graph (FDG), which is a type of compact representation of a set of attributed graphs (AGs) that borrow from Random Graphs the capability of probabilistic modelling of structural and…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…