Related papers: Additive Edge Labelings

A dominating induced matching, also called an efficient edge domination, of a graph $G=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges is a subset $F \subseteq E$ of edges in the graph such that no two edges in $F$ share a common endpoint…

We study \emph{edge-sum distinguishing labeling}, a type of labeling recently introduced by Tuza in [Zs. Tuza, \textit{Electronic Notes in Discrete Mathematics} 60, (2017), 61-68] in context of labeling games. An \emph{ESD labeling} of an…

The super edge-magicness of graphs of equal order and size has been shown to be important since such graphs can be used as seeds to answer many questions related to (super) edge-magic labelings and other types of well studied labelings, as…

We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…

This paper is dedicated to studying the following question: Is it always possible to injectively assign the weights $1,...,|E(G)|$ to the edges of any given graph $G$ (with no component isomorphic to $K_2$) so that every two adjacent…

Let $G$ be a graph with vertex set $V(G)$. Let $n$ and $k$ be non-negative integers such that $n + 2k \leq |V(G)| - 2$ and $|V(G)| - n$ is even. If when deleting any $n$ vertices of $G$ the remaining subgraph contains a matching of $k$…

We generalize some results of $\mathrm{v}$-number for arbitrary monomial ideals by showing that the $\mathrm{v}$-number of an arbitrary monomial ideal is the same as the $\mathrm{v}$-number of its polarization. We prove that the…

We consider a graph polynomial \xi(G;x,y,z) introduced by Averbouch, Godlin, and Makowsky (2007). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Dohmen, Poenitz…

We characterize all graphs whose binomial edge ideals have pure resolutions. Moreover, we introduce a new switching of graphs which does not change some algebraic invariants of graphs, and using this, we study the linear strand of the…

A good edge-labelling of a simple, finite graph is a labelling of its edges with real numbers such that, for every ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. In this paper we prove that any graph on…

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention…

An edge irregular total $k$-labelling $f : V(G)\cup E(G)\rightarrow \{1,2,\dots,k\}$ of a graph $G$ is a labelling of the vertices and the edges of $G$ in such a way that any two different edges have distinct weights. The weight of an edge…

We investigate, using the notion of linear quotients, significative classes of connected graphs whose monomial edge ideals, not necessarily squarefree, have linear resolution, in order to compute standard algebraic invariants of the…

Consider an undirected graph whose edges are labeled invertibly in a group. When does every Eulerian trail from one fixed vertex to another have the same label? We give a precise structural answer to this question. Essentially, we show that…

We call a multigraph $(k,d)$-edge colourable if its edge set can be partitioned into $k$ subgraphs of maximum degree at most $d$ and denote as $\chi'_{d}(G)$ the minimum $k$ such that $G$ is $(k,d)$-edge colourable. We prove that for every…

A \emph{directional labeling} of an edge $\emph{uv}$ in a graph $G=(V,E)$ by an ordered pair $ab$ is a labeling of the edge $uv$ such that the label on $uv$ in the direction from $u$ to $v$ is $\ell(uv)=ab$, and $\ell(vu)=ba$. New…

Let $G$ be a finite simple graph on the vertex set $V(G) = \{x_1, \ldots, x_n\}$ and $I(G) \subset K[V(G)]$ its edge ideal, where $K[V(G)]$ is the polynomial ring in $x_1, \ldots, x_n$ over a field $K$ with each ${\rm deg} x_i = 1$ and…

Simple drawings of graphs are those in which each pair of edges share at most one point, either a common endpoint or a proper crossing. In this paper we study the problem of extending a simple drawing $D(G)$ of a graph $G$ by inserting a…

In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects…

Let $G$ be a graph having a vertex $v$ such that $H = G - v$ is a trivially perfect graph. We give a polynomial-time algorithm for the problem of deciding whether it is possible to add at most $k$ edges to $G$ to obtain a trivially perfect…