Related papers: Graph Labelings Obtainable by Random Walks
A labelled, undirected graph is a graph whose edges have assigned labels, from a specific set. Given a labelled, undirected graph, the well-known minimum labelling spanning tree problem is aimed at finding the spanning tree of the graph…
The theory of rapid mixing random walks plays a fundamental role in the study of modern randomised algorithms. Usually, the mixing time is measured with respect to the worst initial position. It is well known that the presence of…
In an earlier paper the authors proved that limits of convergent graph sequences can be described by various structures, including certain 2-variable real functions called graphons, random graph models satisfying certain consistency…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
Path graphs are intersection graphs of paths in a tree.~In this paper we give a "6\ good characterization" of path graphs, namely, we prove that path graph membership is in $NP\cap CoNP$ without resorting to existing polynomial time…
The study of random walks has increasingly been popular across diverse disciplines such as statistics, mathematics, quantum physics, where they are used to model paths consisting of successive random steps in a mathematical space. A…
Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…
Consider $n$ points distributed uniformly in $[0,1]^d$. Form a graph by connecting two points if their mutual distance is no greater than $r(n)$. This gives a random geometric graph, $\gnrn$, which is connected for appropriate $r(n)$. We…
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$…
Bidirected graphs are multigraphs where every edge has an independent direction at each end. In the paper, with an arbitrary bidirected graph we associate a non-negative integral quadratic form (called the incidence form of the graph), and…
Graph labelling is a key activity of network science, with broad practical applications, and close relations to other network science tasks, such as community detection and clustering. While a large body of work exists on both unsupervised…
An {\em antimagic labeling} of a graph with $m$ edges and $n$ vertices is a bijection from the set of edges to the integers $1,...,m$ such that all $n$ vertex sums are pairwise distinct, where a vertex sum is the sum of labels of all edges…
We consider the following problem arising from the study of human problem solving: Let $G$ be a vertex-weighted graph with marked "in" and "out" vertices. Suppose a random walker begins at the in-vertex, steps to neighbors of vertices with…
A close relation between hitting times of the simple random walk on a graph, the Kirchhoff index, resistance-centrality, and related invariants of unicyclic graphs is displayed. Combining with the graph transformations and some other…
Large scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modeled using network graphs. Valuable insight can be gained by measuring the similarity…
Graph is an important data representation which occurs naturally in the real world applications \cite{goyal2018graph}. Therefore, analyzing graphs provides users with better insights in different areas such as anomaly detection…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
In this paper, we prove that in every 2-tough 2$K_2$-free graph, there is a 2-walk.
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
A class of graphs is called block-stable when a graph is in the class if and only if each of its blocks is. We show that, as for trees, for most $n$-vertex graphs in such a class, each vertex is in at most $(1+o(1)) \log n / \log\log n$…