A Mathematical Approach on Representation of Competitions: Competition Cluster Hypergraphs

Mathematical Problems in Engineering. 2020;2020 DOI 10.1155/2020/2517415


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Journal Title: Mathematical Problems in Engineering

ISSN: 1024-123X (Print); 1563-5147 (Online)

Publisher: Hindawi Limited

LCC Subject Category: Technology: Engineering (General). Civil engineering (General) | Science: Mathematics

Country of publisher: United Kingdom

Language of fulltext: English

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Sovan Samanta (Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, WB-721636, India)

G. Muhiuddin (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abdulaziz M. Alanazi (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia)

Kousik Das (Department of Mathematics, D. J. H. School, Dantan, WB-721451, India)


Blind peer review

Editorial Board

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Time From Submission to Publication: 26 weeks


Abstract | Full Text

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.