On edge product hypergraphs

Document Type : Research Paper

Authors

1 Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, 425 001, India

2 Department of Mathematics, School of Mathematical Sciences, Kavayitri Bahinabai Chaudhari North Maharashtra University Jalgaon-425 001, India

Abstract

In this paper we introduced the notion of an edge product hypergraph. A hypergraph H is said to be an edge product
hypergraph if edges of hypergraph can be labeled with distinct positive integers such that the product of all the labels of edges incident to a vertex is again an edge label of H and if the product of any collection of edges is a label of an edge in H then, they are incident to a vertex. Here we have proved some important results by which one can verify that given hypergraph is a unit edge product hypergraph or not. We also found some results on domination number and inverse domination number of edge product hypergraph and its complement. 

Keywords

References

[1] C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, 1973.
[2] C. Berge, Hypergraphs, Combinatorics of Finite Sets, North-Holland, Amsterdam, 1989.
[3] Bibin K. Jose, Zs. Tuza, Hypergraph Domination and Strong Independence, Appl. Anal. Discrete Math., 3 (2009), 347-358.
[4] Gallian Joseph A, A dynamic survey of graph labelling, Electronic J. Combin., 16 (2000), 39{48.
[5] F. Harary, Sum graphs and di erence graphs, Congress. Numer., 72 (1990), 101-108.
[6] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs Inter Nat. Symposium, Rome, July 1966, Gordon and N.Y.Breach and Dunod, Paris, (1988) 349-355.
[7] Thavamani J. P. and Ramesh D.S.T., Edge product graphs and its properties, The IUP Journal of Computational Mathematics, 4 (2011), 30-38.
Journal of Hyperstructures
Volume 10, Issue 1
June 2021
Pages 1-12

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