Related papers: Network reliability in hamiltonian graphs
Graph neural networks have been shown to be very effective in utilizing pairwise relationships across samples. Recently, there have been several successful proposals to generalize graph neural networks to hypergraph neural networks to…
This paper uses the reliability polynomial, introduced by Moore and Shannon in 1956, to analyze the effect of network structure on diffusive dynamics such as the spread of infectious disease. We exhibit a representation for the reliability…
The toughness of a noncomplete graph $G$ is the maximum real number $t$ such that the ratio of $|S|$ to the number of components of $G-S$ is at least $t$ for every cutset $S$ of $G$, and the toughness of a complete graph is defined to be…
Let $t>0$ be a real number and $G$ be a graph. We say $G$ is $t$-tough if for every cutset $S$ of $G$, the ratio of $|S|$ to the number of components of $G-S$ is at least $t$. Determining toughness is an NP-hard problem for arbitrary…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
In this paper we relate the location of the complex zeros of the reliability polynomial to parameters at which a certain family of rational functions derived from the reliability polynomial exhibits chaotic behaviour. We use this connection…
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values…
A graph $X$ is said to be a pattern polynomial graph if its adjacency algebra is a coherent algebra. In this study we will find a necessary and sufficient condition for a graph to be a pattern polynomial graph. Some of the properties of the…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated. For a given undirected graph $G$, the network failure probability is the probability that…
Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the…
As a result of the interaction of rapid development and competition in information technologies, the reliability of a network and how solid it remains is important. It is called the hat vulnerability of the network to measure the endurance…
In this paper, the concept of cyclic subsets in graph theory is introduced. An interesting theorem which relates to the collective Hamiltonicity of these cyclic subsets in graphs is also presented. This paper uses this theorem to construct…
A graph is Hamiltonian if it contains a cycle which passes through every vertex of the graph exactly once. A classical theorem of Dirac from 1952 asserts that every graph on $n$ vertices with minimum degree at least $n/2$ is Hamiltonian. We…
The hypergraph unreliability problem asks for the probability that a hypergraph gets disconnected when every hyperedge fails independently with a given probability. For graphs, the unreliability problem has been studied over many decades,…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…
The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some…
There is a sizable literature on investigating the minimum and maximum numbers of cycles in a class of graphs. However, the answer is known only for special classes. This paper presents a result on the smallest number of cycles in…
In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary…
A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…