相关论文: On some automorphism related parameters in graphs

The area of graph property testing seeks to understand the relation between the global properties of a graph and its local statistics. In the classical model, the local statistics of a graph is defined relative to a uniform distribution…

Motivated by various data science applications including de-anonymizing user identities in social networks, we consider the graph alignment problem, where the goal is to identify the vertex/user correspondence between two correlated graphs.…

A new notion of vertex independence and rank for a finite graph G is introduced. The independence of vertices is based on the boolean independence of columns of a natural boolean matrix associated to G. Rank is the cardinality of the…

Let $G_{g,b}$ be the set of all uni/trivalent graphs representing the combinatorial structures of pant decompositions of the oriented surface of genus $g$ with $b$ boundary components. We describe the set $A_{g,b}$ of all automorphisms of…

We introduce a class of parameterised counting problems on graphs, p-#Induced Subgraph With Property(\Phi), which generalises a number of problems which have previously been studied. This paper focusses on the case in which \Phi defines a…

We consider a matching problem in a bipartite graph $G$ where every vertex has a capacity and a strict preference order on its neighbors. Furthermore, there is a cost function on the edge set. We assume $G$ admits a perfect matching, i.e.,…

The defect morphology is an essential aspect of the evolution of crystals' microstructure and its response to stress. Existing methods either only report defect concentration or characterize only some of the defect morphologies. The need…

We construct a fixed parameter algorithm parameterized by d and k that takes as an input a graph G' obtained from a d-degenerate graph G by complementing on at most k arbitrary subsets of the vertex set of G and outputs a graph H such that…

A good edge-labeling (gel for short) of a graph $G$ is a function $\lambda: E(G) \to \mathbb{R}$ such that, for any ordered pair of vertices $(x, y)$ of $G$, there do not exist two distinct increasing paths from $x$ to $y$, where…

We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le…

In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…

This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…

The survey provides an overview of the developing area of parameterized algorithms for graph modification problems. We concentrate on edge modification problems, where the task is to change a small number of adjacencies in a graph in order…

Two independent sets of a graph are adjacent if they differ on exactly one vertex (i.e. we can transform one into the other by adding or deleting a vertex). Let $k$ be an integer. We consider the reconfiguration graph $TAR_k(G)$ on the set…

A graph $G$ is a \emph{cover} of a graph $F$ if there exists an onto mapping $\pi : V(G) \to V(F)$, called a (\emph{covering}) \emph{projection}, such that $\pi$ maps the neighbours of any vertex $v$ in $G$ bijectively onto the neighbours…

Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

Call a colouring of a graph distinguishing if the only automorphism which preserves it is the identity. We investigate the role of the Axiom of Choice in the existence of certain proper or distinguishing colourings in both vertex and edge…

We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the…

Traditionally, graph quality metrics focus on readability, but recent studies show the need for metrics which are more specific to the discovery of patterns in graphs. Cluster analysis is a popular task within graph analysis, yet there is…