Related papers: On Integer Additive Set-Filtered Graphs
Given a graph $G=(V,E)$, the longest induced path problem asks for a maximum cardinality node subset $W\subseteq V$ such that the graph induced by $W$ is a path. It is a long established problem with applications, e.g., in network analysis.…
The fixing number of a graph $G$ is the order of the smallest subset $S$ of its vertex set $V(G)$ such that stabilizer of $S$ in $G$, $\Gamma_{S}(G)$ is trivial. Let $G_{1}$ and $G_{2}$ be disjoint copies of a graph $G$, and let…
In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph…
Which graphs admit an integer value harmonic function which is injective and surjective onto $\Z$? Such a function, which we call harmonic labeling, is constructed when the graph is the $\Z^2$ square grid. It is shown that for any finite…
The majority of popular graph kernels is based on the concept of Haussler's $\mathcal{R}$-convolution kernel and defines graph similarities in terms of mutual substructures. In this work, we enrich these similarity measures by considering…
The concept of sum labelling was introduced in 1990 by Harary. A graph is a sum graph if its vertices can be labelled by distinct positive integers in such a way that two vertices are connected by an edge if and only if the sum of their…
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This work applies the IF approach to arrive at a…
We study the problem of computing shortest path or distance between two query vertices in a graph, which has numerous important applications. Quite a number of indexes have been proposed to answer such distance queries. However, all of…
Integrating the special electromagnetic characteristics of Synthetic Aperture Radar (SAR) in deep neural networks is essential in order to enhance the explainability and physics awareness of deep learning. In this paper, we first propose a…
In this paper, we consider two ways of breaking a graph's symmetry: distinguishing labelings and fixing sets. A distinguishing labeling $\phi$ of $G$ colors the vertices of $G$ so that the only automorphism of the labeled graph $(G, \phi)$…
Graph contrastive learning (GCL) has recently achieved substantial advancements. Existing GCL approaches compare two different ``views'' of the same graph in order to learn node/graph representations. The underlying assumption of these…
We study the question of ``how robust are the known lower bounds of labeling schemes when one increases the number of consulted labels''. Let $f$ be a function on pairs of vertices. An $f$-labeling scheme for a family of graphs $\cF$ labels…
Graph neural networks (GNNs) achieve strong performance on homophilic graphs but often struggle under heterophily, where adjacent nodes frequently belong to different classes. We propose an interpretable and adaptive framework for…
For a group $\Gamma$, a $\Gamma$-labelled graph is an undirected graph $G$ where every orientation of an edge is assigned an element of $\Gamma$ so that opposite orientations of the same edge are assigned inverse elements. A path in $G$ is…
The classic enumerative functions for counting colorings of a graph $G$, such as the chromatic polynomial $P(G,k)$, do so under the assumption that the given graph is labeled. In 1985, Hanlon defined and studied the chromatic polynomial for…
A large number of graph invariants of the form $\sum_{uv \in E(G)} F(d_u,d_v)$ are studied in mathematical chemistry, where $uv$ denotes the edge of the graph $G$ connecting the vertices $u$ and $v$, and $d_u$ is the degree of the vertex…
In this paper, we propose an end-to-end graph learning framework, namely Deep Iterative and Adaptive Learning for Graph Neural Networks (DIAL-GNN), for jointly learning the graph structure and graph embeddings simultaneously. We first cast…
Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop…
Graph contrastive learning defines a contrastive task to pull similar instances close and push dissimilar instances away. It learns discriminative node embeddings without supervised labels, which has aroused increasing attention in the past…
Graph embedding is a central problem in social network analysis and many other applications, aiming to learn the vector representation for each node. While most existing approaches need to specify the neighborhood and the dependence form to…