A stochastic telegraph equation is defined by adding a random inhomogeneity to the classical (second order linear hyperbolic) telegraph differential equation. The inhomogeneities we consider are proportional to the two-dimensional white noise, and so...
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We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators and also...
Wounds in epithelial tissues compromise their vital role in homeostasis. A rapid and efficient wound healing encompasses different mechanisms, which includes the formation of a contractile actin-myosin cable around its edge, known as the purse-string...
In a series of papers, we have proposed a non-perturbative field-theoretic approach to deal with strong electron-phonon and strong Coulomb interactions. The key ingredient of such an approach is to determine the full fermion-boson vertex corrections...
The Prüfer code is a bijection between trees on the vertex set $[n]$ and strings on the set $[n]$ of length $n-2$ (Prüfer strings of order $n$). In this paper we examine the `locality' properties of the Prüfer code, i.e. the effect of changing a...
Let $Γ=Γ(A)$ denote a simple strongly connected digraph with vertex set $X$, diameter $D$, and let $\{A_0,A:=A_1,A_2,\ldots,A_D\}$ denote the set of distance-$i$ matrices of $Γ$. Let $\{R_i\}_{i=0}^D$ denote a partition of $X\times X$, where $R_i=...
Let $c$ be an edge-colouring of a graph $G$ such that for every vertex $v$ there are at least $d \ge 2$ different colours on edges incident to $v$. We prove that $G$ contains a properly coloured path of length 2d or a properly coloured cycle of lengt...
We investigate orbifold constructions of conformal field theories from lattices by no-fixed-point automorphisms (NFPA's) $Z_p$ for $p$ prime, $p>2$, concentrating on the case $p=3$. Explicit expressions are given for most of the relevant vertex opera...
A graph $G$ is $α$-excellent if every vertex of $G$ is contained in some maximum independent set of $G$. In this paper, we characterize $α$-excellent bipartite graphs, $α$-excellent unicyclic graphs, $α$-excellent simplicial graphs, $α$-excellen...
We define Leavitt path algebras of hypergraphs generalizing simultaneously Leavitt path algebras of finitely separated graphs and Leavitt path algebras of row-finite vertex-weighted graphs. We find linear bases for those algebras, compute their Gelfa...
The smallest set of vertices needed to differentiate or categorize every other vertex in a graph is referred to as the graph's metric dimension. Finding the class of graphs for a particular given metric dimension is an NP-hard problem. This concept h...
The concept of an identifying code for a graph was introduced by Karpovsky, Chakrabarty, and Levitin in 1998 as the problem of covering the vertices of a graph such that we can uniquely identify any vertex in the graph by examining the vertices that...
A Roman dominating function for a (non-weighted) graph $G=(V,E)$, is a function $f:V\rightarrow \{0,1,2\}$ such that every vertex $u\in V$ with $f(u)=0$ has at least {one} neighbor $v\in V$ such that $f(v)=2$. The minimum weight $\sum_{v\in V}f(v)$ o...
Suppose the vertices of a graph $G$ were labeled arbitrarily by positive integers, and let $Sum(v)$ denote the sum of labels over all neighbors of vertex $v$. A labeling is lucky if the function $Sum$ is a proper coloring of $G$, that is, if we have...
Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date, two-dimensional ver...
Look up node in Wiktionary, the free dictionary. In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex). Node may refer
We propose an exact algorithm for the Graph Burning Problem ($\texttt{GBP}$), an NP-hard optimization problem that models the spread of influence on social networks. Given a graph $G$ with vertex set $V$, the objective is to find a sequence of $k$ ve...
We prove that the spanning trees of any outerplanar triangulation $G$ can be listed so that any two consecutive spanning trees differ in an exchange of two edges that share an end vertex. For outerplanar graphs $G$ with faces of arbitrary lengths (no...
Thin metallic shallow spherical diaphragms are being used for measuring pneumatic pressure in process industries. The drift in vertex realized due to application of pressure is transformed into electrical signal and this is calibrated for pressure. W...