Related papers: Weak harmonic labeling of graphs and multigraphs
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We introduce the concept of link-irregular labelings for graphs, extending the notion of link-irregular graphs through edge labeling with positive integers. A labeling is link-irregular if every vertex has a uniquely labeled subgraph…
Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…
We develop a formalism to address statistical pattern recognition of graph valued data. Of particular interest is the case of all graphs having the same number of uniquely labeled vertices. When the vertex labels are latent, such graphs are…
Graph classification plays a pivotal role in various domains, including pathology, where images can be represented as graphs. In this domain, images can be represented as graphs, where nodes might represent individual nuclei, and edges…
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…
This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying themes of our investigation are various `nonpositive…
For a graph $H$, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions $W$ in $L^p$, $p\geq e(H)$, denoted by $t(H,W)$. One may then define corresponding functionals…
We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We introduce a…
Node classification is an important problem in graph data management. It is commonly solved by various label propagation methods that work iteratively starting from a few labeled seed nodes. For graphs with arbitrary compatibilities between…
In a signed graph $G$, an induced subgraph is called a negative clique if it is a complete graph and all of its edges are negative. In this paper, we give the characteristic polynomials and the eigenvalues of some signed graphs having…
The study of very large graphs is a prominent theme in modern-day mathematics. In this paper we develop a rigorous foundation for studying the space of finite labelled graphs and their limits. These limiting objects are naturally countable…
Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…
A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The…
Consider a simple locally finite hypergraph on a countable vertex set, where each edge represents one unit of load which should be distributed among the vertices defining the edge. An allocation of load is called balanced if load cannot be…
In this paper, firstly, we introduce a higher-dimensional analogue of hypergraphs, namely $\omega$-hypergraphs. This notion is thoroughly flexible because unlike ordinary $\omega$-graphs, an n-dimensional edge called an n-cell has many…
Motivated by the study of greedy algorithms for graph coloring, we introduce a new graph parameter, which we call weak degeneracy. By definition, every $d$-degenerate graph is also weakly $d$-degenerate. On the other hand, if $G$ is weakly…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
A sum graph is a finite simple graph whose vertex set is labeled with distinct positive integers such that two vertices are adjacent if and only if the sum of their labels is itself another label. The spum of a graph $G$ is the minimum…
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…