Related papers: On the decomposition of connected graphs into thei…
The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
In this paper we investigate the connectedness and the isomorphism problems for zig-zag products of two graphs. A sufficient condition for the zig-zag product of two graphs to be connected is provided, reducing to the study of the…
In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…
Unigraphs are graphs identifiable up to isomorphism from their degree sequences. Given a class $\mathcal{A}$ of graphs, we define the class of $\mathcal{A}$-unigraphs to be graphs identifiable from degree sequence and membership in…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
The graph reconstruction problem has been extensively studied under various query models. In this paper, we propose a new query model regarding the number of connected components, which is one of the most basic and fundamental graph…
We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…
Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…
In this paper, we study oriented bipartite graphs. In particular, we introduce "bitransitive" graphs. Several characterizations of bitransitive bitournaments are obtained. We show that bitransitive bitounaments are equivalent to acyclic…
This paper describes a new approach to the problem of generating the class of all geodetic graphs homeomorphic to a given geodetic one. An algorithmic procedure is elaborated to carry out a systematic finding of such a class of graphs. As a…
We offer a new structural basis for the theory of 3-connected graphs, providing a unique decomposition of every such graph into parts that are either quasi 4-connected, wheels, or thickened $K_{3,m}$'s. Our construction is explicit,…
The decomposition of undirected graphs simplifies complex problems by breaking them into solvable subgraphs, following the philosophy of divide and conquer. This paper investigates the relationship between atom decomposition and the maximum…
We describe the full automorphism group of the directed reduced power graph and the undirected reduced power graph of a finite group. We compute the full automorphism groups of these graphs of several classes of finite groups. Also, we…
By a well known theorem of Robbins, a graph $G$ has a strongly connected orientation if and only if $G$ is 2-edge-connected and it is easy to find, in linear time, either a cut edge of $G$ or a strong orientation of $G$. A result of Durand…
In this note we present an infinite family of 2-connected graphs such that their matching polynomials have only integer zeros. This answers in negative a question of Akbari et al. [Graphs with integer matching polynomial zeros, Discrete…
A connected undirected graph $G=(V,E)$ is given. This paper presents an algorithm that samples (non-uniformly) a $K$ partition $U_1,\ldots U_K$ of the graph nodes $V$, such that the subgraph induced by each $U_k$, with $k=1:K$, is…
We compute numerically the homology of several graph complexes in low loop orders, extending previous results.
The problem of finding the connected components of a graph is considered. The algorithms addressed to solve the problem are used to solve such problems on graphs as problems of finding points of articulation, bridges, maximin bridge, etc. A…
Any graph which is not vertex transitive has a proper induced subgraph which is unique due to its structure or the way of its connection to the rest of the graph. We have called such subgraph as an anchor. Using an anchor which, in fact, is…