Search

We consider the notion of χ -completeness of a locally finite graph and we extend this notion to the weighted magnetic graph. Moreover, we establish a link between the magnetic adjacency matrix on line graph and the magnetic discrete Laplacian on 1-forms. [ABSTRACT FROM AUTHOR]

Connected planar graphs are of interest to a variety of scholars. Being able to simulate a database of such graphs with selected properties would support specific types of inference for spatial analysis and other network-based disciplines. This paper presents a simple, efficient, and flexible connected planar graph generator for this purpose. It also summarizes a comparison between an empirical set of specimen graphs and their simulated counterpart set, and establishes evidence for positing a conjecture about the principal eigenvalue of connected planar graphs. Finally, it summarizes a probability assessment of the algorithm’s outcomes as well as a comparison between the new algorithm and selected existing planar graph generators. [ABSTRACT FROM AUTHOR]

In this paper, a tolerance representation model for generating tolerance specification schemes and corresponding tolerance zones is proposed to meet the requirement of the representation of tolerance information semantics. This model is hierarchically organized and consists of five layers. They are component, geometric feature, variational geometric constraint, tolerance specification scheme, and tolerance zone layers. The mating relations between components in the component layer, the mating relations between geometric features in the geometric feature layer, the variational geometric constraints between geometric features in the variational geometric constraint layer, the tolerance specification schemes of component in the tolerance specification scheme layer, and the tolerance zones of tolerance specification schemes in the tolerance zone layer are formally defined by one or more adjacency matrices, respectively. Based on the model, a method for generating tolerance specification schemes for component and their resultant tolerance zones is designed. This method shows how to adopt a top-down strategy to carry out tolerance specification for an arbitrary assembly designed in a CAD system. The paper also provides a practical example to illustrate how the method works. [ABSTRACT FROM AUTHOR]

A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines. [ABSTRACT FROM AUTHOR]

We study spectral properties of the Manhattan products of the path graphs and show the concentration of zero-eigenvelues. [ABSTRACT FROM AUTHOR]

The Hoffman-Singleton graph is the unique strongly regular graph with parameters (50, 7, 0, 1). A well-known hypothesis states that a distance-regular graph in which the neighborhood of each vertex is isomorphic to the Hoffman-Singleton graph has intersection array {50, 42, 1; 1, 2, 50} or {50, 42, 9; 1, 2, 42}. In the present paper, we prove this hypothesis under the assumption that a distance-regular graph is a Terwilliger graph and the graph diameter is at most 5. [ABSTRACT FROM AUTHOR]

Possible orders and fixed-point subgraphs of automorphisms of a generalized octagon of order (2, 4) are found. The vertex-symmetric generalized octagon of order (2, 4) is proved to be classical. [ABSTRACT FROM AUTHOR]

This paper presents a new MSDI (mold surface data integration) method for presenting ruled mold-surface data for CAPP applications. The method makes use of adjacency and feature-data matrices to establish a framework of feature-based data. The MSDI method enables the storage, retrieval and operations of geometries, topologies, and machining information of a given ruled mold surface. The matrices of adjacency and feature-data effectively represent the relations. Boolean algebra and group technology (GT) methods are introduced to generate the desired process plans. A sample mold made of ruled surfaces is made and used to show the effectiveness of the proposed data representation and the integrated mold surface processing method. A compact computer program is implemented to enhance the speed and accuracy of the MSDI method. The numerical results indicate that the mold surface decomposition and integration procedure presented in this paper are systematic and effective. The paper provides a novel modular mold surface modeling tool and procedure that can be further extended to accommodate more features appearing in complicated ruled mold surfaces. [ABSTRACT FROM AUTHOR]

It is proved that any set of finite pairwise nonisomorphic weakly cospectral connected pseudographs, as well as any set of pseudodigraphs satisfying various additional conditions, is finite. [ABSTRACT FROM AUTHOR]