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We propose a simple yet effective method for detecting anomalous instances on an attribute graph with label information of a small number of instances. Although with standard anomaly detection methods it is usually assumed that instances…

Foucaud et al. [Discrete Appl. Math. 319 (2022), 424-438] recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. For a set $M$ of vertices and an edge $e$ of a graph $G$, let $P(M,…

This paper proposes a blind detection problem for low pass graph signals. Without assuming knowledge of the exact graph topology, we aim to detect if a set of graph signal observations are generated from a low pass graph filter. Our problem…

In software, a vulnerability is a defect in a program that attackers might utilize to acquire unauthorized access, alter system functions, and acquire information. These vulnerabilities arise from programming faults, design flaws, incorrect…

This study explores the effectiveness of graph neural networks (GNNs) for vulnerability detection in software code, utilizing a real-world dataset of Java vulnerability-fixing commits. The dataset's structure, based on the number of…

Detecting unusual patterns in graph data is a crucial task in data mining. However, existing methods face challenges in consistently achieving satisfactory performance and often lack interpretability, which hinders our understanding of…

The one-class classification problem is a well-known research endeavor in pattern recognition. The problem is also known under different names, such as outlier and novelty/anomaly detection. The core of the problem consists in modeling and…

The all-terminal reliability of a graph $G$ is the probability that $G$ remains connected when each edge fails independently with probability $p$. For fixed $n$ and $m$, the uniformly most reliable problem asks which graph with $n$ vertices…

This paper introduces a new class of efficient inter connection networks called as M-graphs for large multi-processor systems.The concept of M-matrix and M-graph is an extension of Mn-matrices and Mn-graphs.We analyze these M-graphs…

It is now well known that the performance of a linear code $C$ under iterative decoding on a binary erasure channel (and other channels) is determined by the size of the smallest stopping set in the Tanner graph for $C$. Several recent…

This paper investigates runtime monitoring of perception systems. Perception is a critical component of high-integrity applications of robotics and autonomous systems, such as self-driving cars. In these applications, failure of perception…

Fault-tolerant complexes describe surface-code fault-tolerant protocols from a single geometric object. We first introduce fusion complexes that define a general family of fusion-based quantum computing (FBQC) fault-tolerant quantum…

Cops and Robbers is a type of pursuit-evasion game played on a graph where a set of cops try to capture a single robber. The cops first choose their initial vertex positions, and later the robber chooses a vertex. The cops and robbers make…

An edge-coloring of a graph $G$ with colors $1,\ldots,t$ is an \emph{interval $t$-coloring} if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an integer interval. It is well-known that…

Minimal separators in graphs are an important concept in algorithmic graph theory. In particular, many problems that are NP-hard for general graphs are known to become polynomial-time solvable for classes of graphs with a polynomially…

We initiate the study on fault-tolerant spanners in hypergraphs and develop fast algorithms for their constructions. A fault-tolerant (FT) spanner preserves approximate distances under network failures, often used in applications like…

We introduce the \emph{ID-index} of a finite simple connected graph. For a graph $G=(V,\ E)$ with diameter $d$, we let $f:V\longrightarrow \mathbb{R}$ assign \emph{ranks} to the vertices, then under $f$, each vertex $v$ gets a…

The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform scenario set. Such a scenario set assumes that every subset of the network resources (edges or vertices) of a given cardinality $k$ comprises a…

Graph neural networks can be effectively applied to find solutions for many real-world problems across widely diverse fields. The success of graph neural networks is linked to the message-passing mechanism on the graph, however, the…

Adversarial attacks can affect the performance of existing deep learning models. With the increased interest in graph based machine learning techniques, there have been investigations which suggest that these models are also vulnerable to…