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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.…
Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is…
Graph neural networks (GNN) have been successful in many fields, and derived various researches and applications in real industries. However, in some privacy sensitive scenarios (like finance, healthcare), training a GNN model centrally…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
Understanding why neural networks make certain decisions is pivotal for their use in safety-critical applications. Feature-Guided Analysis (FGA) extracts slices of neural networks relevant to their tasks. Existing feature-guided approaches…
A locating-dominating set of a graph $G$ is a dominating set of $G$ such that every vertex of $G$ outside the dominating set is uniquely identified by its neighborhood within the dominating set. The location-domination number of $G$ is the…
Topological indices play a vital role in the area of graph theory and fuzzy graph (FG) theory. It has wide applications in the areas such as chemical graph theory, mathematical chemistry, etc. Topological indices produce a numerical…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
Federated Learning (FL) deals with learning a central model (i.e. the server) in privacy-constrained scenarios, where data are stored on multiple devices (i.e. the clients). The central model has no direct access to the data, but only to…
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
We present a new probabilistic modelling framework based on the recent notion of normal factor graph (NFG). We show that the proposed NFG models and their transformations unify some existing models such as factor graphs, convolutional…
The necessary integration of renewable energy sources, combined with the expanding scale of power networks, presents significant challenges in controlling modern power grids. Traditional control systems, which are human and…
In communication networks, the binding numbers of graphs (or networks) are often used to measure the vulnerability and robustness of graphs (or networks). Furthermore, the fractional factors of graphs and the fractional…
Vision foundation models (FMs) have become the predominant architecture in computer vision, providing highly transferable representations learned from large-scale, multimodal corpora. Nonetheless, they exhibit persistent limitations on…
Directed acyclic graphs (DAGs) are a class of graphs commonly used in practice, with examples that include electronic circuits, Bayesian networks, and neural architectures. While many effective encoders exist for DAGs, it remains…
Federated Graph Learning (FGL) is an emerging technology that enables clients to collaboratively train powerful Graph Neural Networks (GNNs) in a distributed manner without exposing their private data. Nevertheless, FGL still faces the…
As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given…
Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…
Graph learning has a wide range of applications in many scenarios, which require more need for data privacy. Federated learning is an emerging distributed machine learning approach that leverages data from individual devices or data centers…