A characterization of cube-hypergraphs

“…Specially, Berge (1961Berge ( ,1973Berge ( , 1989 introduced hypergraphs as a generalization of graphs. Buroscha and Ceccherini (1996) characterized cubehypergraphs where each hyperedge contains three vertices. Tyshkevich and Zverovich (1996) introduced a new multivalued function, the line hypergraph.…”

Section: Introductionmentioning

confidence: 99%

“…Buroscha and Ceccherini ( 1996 ) characterized cube-hypergraphs where each hyperedge contains three vertices. Tyshkevich and Zverovich ( 1996 ) introduced a new multivalued function, the line hypergraph.…”

Section: Introductionmentioning

confidence: 99%

A study of cluster hypergraphs and its properties

Maity¹,

Das²,

Samanta³

et al. 2021

Soc. Netw. Anal. Min.

View full text Add to dashboard Cite

In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where cluster nodes are allowed. Few related terms and properties on cluster hypergraphs are discussed. Some operations, including the Cartesian product, union, intersection, etc., are studied. Different types of matrix representations and isomorphism are also proposed on cluster hypergraphs. The notion of an effective degree for nodes is introduced to capture the group/ cluster effects. At last, the area of applications and future directions with conclusions is deployed.

show abstract

“…Burosch and Ceccherini [13] characterised cube hypergraphs, where each hyperedge contains three vertices. Bergen et al [14] studied infection in hypergraphs.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Approach on Representation of Competitions: Competition Cluster Hypergraphs

Samanta¹,

Muhiuddin

Alanazi

et al. 2020

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Social networks are represented using graph theory. In this case, individuals in a social network are assumed as nodes. Sometimes institutions or groups are also assumed as nodes. Institutions and such groups are assumed as cluster nodes that contain individuals or simple nodes. Hypergraphs have hyperedges that include more than one node. In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where cluster nodes are allowed. Sometimes competitions in the real world are done as groups. Cluster hypergraphs are used to represent such kinds of competitions. Competition cluster hypergraphs of semidirected graphs (a special type of mixed graphs called semidirected graphs, where the directed and undirected edges both are allowed) are introduced, and related properties are discussed. To define competition cluster hypergraphs, a few properties of semidirected graphs are established. Some associated terms on semidirected graphs are studied. At last, a numerical application is illustrated.

show abstract

A characterization of cube-hypergraphs

Cited by 5 publications

References 9 publications

On the spectrum of hypergraphs

On the spectrum of hypergraphs

A study of cluster hypergraphs and its properties

A Mathematical Approach on Representation of Competitions: Competition Cluster Hypergraphs

Contact Info

Product

Resources

About