Related papers: Some inner metric parameters of a digraph: Iterate…
The class of closed graphs by a linear ordering on their sets of vertices is investigated. A recent characterization of such a class of graphs is analyzed by using tools from the proper interval graph theory.
The class of intersection bigraphs of unit intervals of the real line whose ends may be open or closed is called a class of mixed unit interval bigraphs. This class of bigraphs is a strict superclass of the class of unit interval bigraphs.…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…
Radial Moore graphs and digraphs are extremal graphs related to the Moore ones where the distance-preserving spanning tree is preserved for some vertices. This leads to classify them according to their proximity to being a Moore graph or…
Let $G$ be a finite simple non-complete connected graph on $\{1, \ldots, n\}$ and $\kappa(G) \geq 1$ its vertex connectivity. Let $f(G)$ denote the number of free vertices of $G$ and $\mathrm{diam}(G)$ the diameter of $G$. Being motivated…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
Given a digraph $G$, we propose a new method to find the recurrence equation for the number of vertices $n_k$ of the $k$-iterated line digraph $L^k(G)$, for $k\geq0$, where $L^0(G)=G$. We obtain this result by using the minimal polynomial…
Integral circulant graphs are proposed as models for quantum spin networks that permit a quantum phenomenon called perfect state transfer. Specifically, it is important to know how far information can potentially be transferred between…
We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to…
We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…
We examine the capacity of the complementarity spectrum to distinguish non-isomorphic digraphs. We focus on the seven families with exactly three complementarity eigenvalues. Our findings reveal that in some, but not all families, any two…
Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…
This article investigates the properties of order-divisor graphs associated with finite groups. An order-divisor graph of a finite group is an undirected graph in which the set of vertices includes all elements of the group, and two…
We introduce a broad class of equations that are described by a graph, which includes many well-studied systems. For these, we show that the number of solutions (or the dimension of the solution set) can be bounded by studying certain…
The inclusion ideal graph of a commutative unitary ring $R$ is the (undirected) graph $In(R)$ whose vertices all non-trivial ideals of $R$ and two distinct vertices are adjacent if and only if one of them is a proper subset of the other…
A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…
Two problems in the search of metric characteristics on weighted undirected graphs with non-negative edge weights are being considered. The first problem: a weighted undirected graph with non-negative edge weight is given. The radius,…
In this note we study and compare three graph invariants related to the 'compactness' of graph drawing in the plane: the dilation coefficient, defined as the smallest possible quotient between the longest and the shortest edge length; the…
This article investigates integer sequences that partition the sequence into blocks of various lengths - irregular arrays. The main result of the article is explicit formulas for numbering of irregular arrays. A generalization of Cantor…
In the theory of line graphs of undirected graphs there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, the exists no analogous…