Related papers: Total embedding distributions of Ringel ladders
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the…
The celebrated formula of Otter \emph{[Ann. of Math. (2) 49 (1948), 583--599]} asserts that the complete graph contains exponentially many non-isomorphic spanning trees. In this paper, we show that every connected almost regular graph with…
When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different…
The exchange graph of a 2-acyclic quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. When the quiver admits a nondegenerate Jacobi-finite potential, the exchange graph admits a natural acyclic…
We show that on a metric graph of genus $g$, a divisor of degree $n$ generically has $g(n-g+1)$ Weierstrass points. For a sequence of generic divisors on a metric graph whose degrees grow to infinity, we show that the associated Weierstrass…
The paper systematically classifies rings based on the dominant metric dimensions (Ddim) of their associated CZDG, establishing consequential bounds for the Ddim of these compressed zero-divisor graphs. The authors investigate the interplay…
This paper considers *-graphs in which all vertices have degree 4 or 6, and studies the question of calculating the genus of orientable 2-surfaces into which such graphs may be embedded. A *-graph is a graph endowed with a formal adjacency…
In the symmetric group on a set of size 2n, let P_{2n} denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as ``pairings'', since each disjoint cycle has length 2). Harer and Zagier explicitly…
This paper is the second part of our comprehensive study on the braid index problem of pretzel links. Our ultimate goal is to completely determine the braid indices of all pretzel links, alternating or non alternating. In our approach, we…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…
The routing and wavelength assignment problem arises from the investigation of optimal wavelength allocation in an optical network that employs Wavelength Division Multiplexing (WDM). Consider an optical network that is represented by a…
We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…
This short note is a supplement to [1], in which the total variation of graph distributional signals is introduced and studied. We introduce a different formulation of total variation and relate it to the notion of edge centrality. The…
We prove that if a tree $T$ has $n$ vertices and maximum degree at most $\Delta$, then a copy of $T$ can almost surely be found in the random graph $\mathcal{G}(n,\Delta\log^5 n/n)$.
When each vertex is assigned a set, the intersection graph generated by the sets is the graph in which two distinct vertices are joined by an edge if and only if their assigned sets have a nonempty intersection. An interval graph is an…
Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it's local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a…
We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
Many real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution of the number of…