Related papers: Weak Dominance Drawings and Linear Extension Diame…
In this paper, we introduce the notion of the weak majority dimension of a digraph which is well-defined for any digraph. We first study properties shared by the weak dimension of a digraph and show that a weak majority dimension of a…
In extension problems of partial graph drawings one is given an incomplete drawing of an input graph $G$ and is asked to complete the drawing while maintaining certain properties. A prominent area where such problems arise is that of…
In this paper we study relations between connected and weakly convex domination numbers. We show that in general the difference between these numbers can be arbitrarily large and we focus on the graphs for which a weakly convex domination…
Weakly distance-regular digraphs is a directed version of distance-regular graphs. In this paper, we characterize all weakly distance-regular digraphs of diameter 2.
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
Using the two way distance, we introduce the concepts of weak metric dimension of a strongly connected digraph $\Gamma$. We first establish lower and upper bounds for the number of arcs in $\Gamma$ by using the diameter and weak metric…
In this paper, we study commutative weakly distance-regular digraphs whose attached association schemes are regular, and give a characterization of mixed arcs. As an application, we classify such digraphs of diameter 2.
In this work, we have introduced and studied some basic geometric properties of extended weakly symmetric spaces. After classification of this structure we have also established the existence of such a space by presenting a non-trivial…
The power dominating set (PDS) problem is the following extension of the well-known dominating set problem: find a smallest-size set of nodes $S$ that power dominates all the nodes, where a node $v$ is power dominated if (1) $v$ is in $S$…
A weak dominance drawing $\Gamma$ of a DAG $G=(V,E)$, is a $d$-dimensional drawing such that there is a directed path from a vertex $u$ to a vertex $v$ in $G$ if $D(u) <D(v)$ for every dimension $D$ of $\Gamma$. We have a \emph{falsely…
The aim of this paper is to investigate weakly developable spaces. For a comparison with semi-metrizable spaces, we introduce and study a class of spaces among those of weakly developable spaces, semimetrizable spaces and first countable…
We investigate here the computational complexity of three natural problems in directed acyclic graphs. We prove their NP Completeness and consider their restrictions to linear orders.
We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…
In this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic. We also present upper bounds for the…
Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information,…
Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we…
The minimum dominating set problem asks for a dominating set with minimum size. First, we determine some vertices contained in the minimum dominating set of a graph. By applying a particular scheme, we ensure that the resulting graph is…
Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear…
Let $G=(V(G),E(G))$ be a simple graph. A non-empty set $S\subseteq V (G)$ is a weakly connected dominating set in $G$, if the subgraph obtained from $G$ by removing all edges each joining any two vertices in $V (G)\setminus S$ is connected.…
This paper initiates the study of fractional eternal domination in graphs, a natural relaxation of the well-studied eternal domination problem. We study the connections to flows and linear programming in order to obtain results on the…