112 Results Found

In this paper we introduce Cayley digraphs associated to finitely generated polygroups, where the vertices correspond to finite products of the generators of polygroups and the edges to multiplication by vertices and generators. We investigate some p...

The following two optimization problems on acyclic digraph analysis are solved. The first of them consists of determining the minimum (in terms of volume) set of arcs, the removal of which from an acyclic digraph breaks all paths passing through a su...

The semigroup D_V of digraphs on a set V of n labeled vertices is defined. It is shown that D_V is faithfully represented by the semigroup B_n of n ´ n Boolean matrices and that the Green’s L, R, H, and D equivalence classifications of digraphs in D_V fo...

Theenergy of a graph is a classical spectral invariant defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. Recently, the notion of local energy was introduced to measure the contribution of vertices to the total ener...

A rough neutrosophic set model is a hybrid model which deals with vagueness by using the lower and upper approximation spaces. In this research paper, we apply the concept of rough neutrosophic sets to graphs. We introduce rough neutrosophic digraphs...

Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS) theory is a hybrid tool for handling uncertain information...

In this paper, we define and characterize the embedding of edges and higher-order entities in directed graphs (digraphs) and relate these embeddings to those of nodes. Our edge-centric approach consists of the following: (a) Embedding line digraphs (...

The principal aim of this article is to initiate a study of the following coloring notion for digraphs. An odd k-edge coloring of a general digraph (directed pseudograph) D is a (not necessarily proper) coloring of its edges with at most k colors suc...

Let G be a strongly connected digraph, and $d_G(v_i,v_j)$ denote the distance from the vertex $v_i$ to vertex $v_j$ and be defined as the length of the shortest directed path from $v_i$ to $v_j$ in G. The sum distance between vertices $v_i$ and $v_j$ in G is defined as $s{d}_G$...

The guessing number of a digraph is a new invariant in graph theory raised by S. Riis in 2006 and based on its applications in network coding and boolean circuit complexity theory. In this paper, we present the lower and upper bounds on a guessing nu...

Practical algorithms for computing canonical forms of multi-digraphs do not exist in the literature. This paper proposes two practical approaches for finding canonical forms, from the perspective of nD symbolic computation. Initially, the approaches...

MSP DAGs (short for minimal series-parallel digraphs) can be defined from the single vertex graph by applying the parallel composition and series composition. We prove an upper bound of 6 for the directed clique-width of MSP DAGs and show how a direc...

Transitive tournament (including transitive triangle) and its blow-up have some symmetric properties. In this work, we establish an analogue result of the Erdös-Stone theorem of weighted digraphs with a forbidden blow-up of the transitive tourna...

A digraph (D) is symmetric if $(u,v)$ is an arc of D and if $(v,u)$ is also an arc of D. If a symmetric digraph is primitive and contains d loops, then it is said to be a symmetric primitive digraph with d loops. The m-competition index (generalized comp...

Let S be a Clifford semigroup and A a subset of S. We write $Cay(S,A)$ for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number of a graph is the maximum cardinality of an (weakly, path, weakly pat...

A vertex-degree-based (VDB, for short) topological index $\phi$ induced by the numbers $\left\{{\phi }_{ij}\right\}$ was recently defined for a digraph D, as ${\displaystyle \phi \left(D\right)=\frac{1}{2}\sum _{uv}{\phi }_{d_u^{+}{d}_v^{-}},}$ where $d_u^{+}$ denotes the out-degree of the vertex $u,$$d_v^{-}$ denotes the in-degree of the vertex $v,$ and the sum ru...

After the initiation of Jachymski’s contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of cont...

Let D be a primitive digraph of order $n.$ The exponent of a vertex x in $V(D)$ is denoted ${\gamma }_D(x),$ which is the smallest integer q such that for any vertex $y,$ there is a walk of length q from x to y. Let $V(D)=\{v_1,v_2,\cdots ,v_n\}.$ We order the vertice...

Let $D{S}_n\left(d\right)$ denote the set of all doubly symmetric primitive digraphs of order n with d loops, where d is an integer and $1\le d\le n.$ In this paper, we determine the upper bounds for the m-competition indices(generalized competition indices) of $D{S}_n\left(d\right)$...

A digraph D is an efficient open domination digraph if there exists a subset S of $V\left(D\right)$ for which the open out-neighborhoods centered in the vertices of S form a partition of $V\left(D\right)$ . In this work we deal with the efficient open dom...

Minimal Strong Digraphs (MSDs) can be regarded as a generalization of the concept of tree to directed graphs. Their cyclic structure and some spectral properties have been studied in several articles. In this work, we further study some properties of...

In this work, two novel methodologies with the ability to address dependence and feedback among criteria and their interrelations are proposed for Cognitive Multi-Criteria Decision Making (CMCDM). Both methods, a modified Fuzzy Digraph approach and a...

This paper investigates the problem of fixed-time distributed time-varying optimization of a nonlinear fractional-order multiagent system (FOMAS) over a weight-unbalanced directed graph (digraph), where the heterogeneous unknown nonlinear functions a...

Let D be a digraph with n vertices and a arcs. The Laplacian and the signless Laplacian matrices of D are, respectively, defined as $L\left(D\right)=De{g}^{+}\left(D\right)-A\left(D\right)$ and $Q\left(D\right)=De{g}^{+}\left(D\right)+A\left(D\right)$, where $A\left(D\right)$ represents the adjacency matrix and $De{g}^{+}\left(D\right)$ represents the d...

In this paper, we focus on methods to prevent shoulder-surfing attacks. We initially adopted digraph substitution rules from PlayFair cipher as our proposed method. PlayFair cipher is a modern cryptography method, which exists at the intersection of...

Let $D=\left(V\right(D),A(D\left)\right)$ be a digraph of order n and let $r\in S\subseteq V\left(D\right)$ with $2\le \left|S\right|\le n$. A directed $(S,r)$-Steiner path (or an $(S,r)$-path for short) is a directed path P beginning at r such that $S\subseteq V\left(P\right)$. Arc-disjoint between two $(S,r)$-paths is cha...

The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph $\mathcal{D}$...

This paper presents a novel theory and method to calculate the canonical labelings of digraphs whose definition is entirely different from the traditional definition of Nauty. It indicates the mutual relationships that exist between the canonical lab...

Let C be any oriented cycle on n vertices. We show that every $(10n-4)$-chromatic digraph spanned by a Hamiltonian directed path contains a subdivision of C.

Let $\mathcal{D}=\left(V\right(\mathcal{D}),A(\mathcal{D}\left)\right)$ be a finite, simple digraph and k a positive integer. A function $f:V\left(\mathcal{D}\right)\to \{0,1,2,\dots ,k+1\}$ is called a $\left[k\right]$-Roman dominating function (for short, $\left[k\right]$-RDF) if $f\left(A{N}^{-}\left[v\right]\right)\ge \left|A{N}^{-}\left(v\right)\right|+k$ for any vertex $v\in V\left(\mathcal{D}\right)$, wher...

Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented graph $$...

Let C be an oriented cycle with two blocks and let n denote the number of its vertices. We show that every $(n+2)$-chromatic digraph spanned by a Hamiltonian directed path contains a subdivision of C. This bound is tight.

A new domination parameter in a fuzzy digraph is proposed to espouse a contribution in the domain of domination in a fuzzy graph and a directed graph. Let $G_D^{*}=\left(V,A\right)$ be a directed simple graph, where $V$ is a finite nonempty set and $A=\left\{\left(x,y\right):x,y\in V,x\ne y\right\}$. A fuz...

Rough set theory and neutrosophic set theory are mathematical models to deal with incomplete and vague information. These two theories can be combined into a framework for modeling and processing incomplete information in information systems. Thus, t...

A D-decomposition of a graph (or digraph) G is a partition of the edge set (or arc set) of G into subsets, where each subset induces a copy of the fixed graph D. Graph decomposition finds motivation in numerous practical applications, particularly in...

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and di...

Among the various generalizations of persistent topology, that based on rank functions and leading to indexing-aware functions appears to be particularly suited to catching graph-theoretical properties without the need for a simplicial construction a...

In this paper, we construct the colored-path homology theory in the category of vertex colored (di)graphs and describe its basic properties. Our construction is based on the path homology theory of digraphs that was introduced in the papers of Grigor...

In this paper, we merge two theories: that of pulse processes on weighted digraphs and that of evolution algebras. We enrich both of them. In fact, we obtain new results in the theory of pulse processes thanks to the new algebraic tool that we introd...

Using the concept of informational digraphs, we propose a “no redundant information sets” property that can characterize the exact class of extensive games which can be time structured. Our result can be applied to define time-dependent s...

This paper aims to identify the negative impacts of the COVID-19 outbreak on supply chains and propose strategies to deal with the impacts in the context of the readymade garment (RMG) industry supply chain of an emerging economy: Bangladesh. To achi...

A VDB (vertex-degree-based) topological index over a set of digraphs $\mathcal{H}$ is a function $\phi :\mathcal{H}\to \mathbb{R}$, defined for each $H\in \mathcal{H}$ as $$\phi \left(H\right)=\frac{1}{2}\sum _{uv\in E}{\phi }_{d_u^{+}{d}_v^{-}},$$ where E is the arc set of H, $d_u^{+}$ and $d_v^{-}$ denote the out-degree and in-de...

In this survey paper, we will present a number of core algorithmic questions concerning several transitive reduction problems on network that have applications in network synthesis and analysis involving cellular processes. Our starting point will be...

This document focuses attention on the fundamental solution of an autonomous linear retarded functional differential equation (RFDE) along with its supporting cast of actors: kernel matrix, characteristic matrix, resolvent matrix; and the Laplace tra...

In this work, the distributed average consensus for dynamical networks with Lipschitz nonlinear dynamics is studied, where the network communication switches quickly among a set of directed and balanced switching graphs. Differing from existing resea...

A graph is a very important structure to describe many applications in the real world. In many applications, such as dependency graphs and debt graphs, it is an important problem to find and remove cycles to make these graphs be cycle-free. The commo...

Opinion polarization, echo chambers, and the rapid formation of opinion clusters have become defining features of debates on contemporary online social platforms. To explain these phenomena from a control-theoretic perspective, this paper investigate...

The prediction of crowd flow in key urban areas is an important basis for city informatization development and management. Timely understanding of crowd flow trends can provide cities with data support in epidemic prevention, public security manageme...

In this paper, we introduce the notion of resolvable networks. A resolvable network is a digraph of subnetworks, where subnetworks may overlap, and the inner structure of subnetworks are not interesting from the viewpoint of the network. There are tw...

This paper investigates distributed optimization problems for multi-agent systems with parametric uncertainties over unbalanced directed communication networks. To settle this class of optimization problems, a continuous-time algorithm is proposed by...