Related papers: Algorithmic aspects of algebraic methods for graph…
We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the…
In this paper, we show the existence of a polynomial time graph isomorphism algorithm for all graphs excluding graphs that are locally trianglefree. This particular class of graphs allows to divide the graph into neighbourhood sub-graph…
Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at…
In this note we prove that every closed graph $G$ is up to isomorphism a proper interval graph. As a consequence we obtain that there exist linear-time algorithms for closed graph recognition.
In the past decades for more and more graph classes the Graph Isomorphism Problem was shown to be solvable in polynomial time. An interesting family of graph classes arises from intersection graphs of geometric objects. In this work we show…
In this paper, we study the graph isomorphism and graph automorphism problems. We propose a novel technique to analyze graph isomorphism and graph automorphism. Further we handled some strongly regular datasets for prove the efficiency of…
Using spectral graph theory, we show how to obtain inequalities for the number of walks in graphs from nonnegative polynomials and present a new family of such inequalities.
Graph theory is a branch of mathematics in which pair-wise relations between objects are studied. My PhD thesis, supervised by David R. Wood, introduces and investigates a new family of graphs, called link graphs, that generalises the…
We show that the quantum dynamics of interacting and noninteracting quantum particles are fundamentally different in the context of solving a particular computational problem. Specifically, we consider the graph isomorphism problem, in…
With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi-labeled…
Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to…
Quantifying the similarity between two graphs is a fundamental algorithmic problem at the heart of many data analysis tasks for graph-based data. In this paper, we study the computational complexity of a family of similarity measures based…
We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of $k$-means in that space is applied. The algorithm is therefore fast and easily…
In this paper, we demonstrate that considering experiments in a graph-theoretic manner allows us to exploit automorphisms of the graph to reduce the number of evaluations of candidate designs for those experiments, and thus find optimal…
This paper presents an exhaustive approach for verification of the weak reconstruction of Self Complementary Graphs up to 17 vertices. It describes the general problem of the Reconstruction Conjecture, explaining the complexity involved in…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
The rise of graph analytic systems has created a need for ways to measure and compare the capabilities of these systems. Graph analytics present unique scalability difficulties. The machine learning, high performance computing, and visual…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
Given a graph $G$, the graph $[G]$ obtained by adding, for each pair of vertices of $G$, a unique vertex adjacent to both vertices is called the binding graph of $G$. In this work, we show that the class of binding graphs is…
Characterizations graphs of some classes to induce periodic Grover walks have been studied for recent years. In particular, for the strongly regular graphs, it has been known that there are only three kinds of such graphs. Here, we focus on…