Hyperideal-based intersection graphs

The purpose of this paper is to introduce the notion of intersection graphs based on non-trivial hyperideals in general hyperrings. In order to realise the article’s goals, we design general hyperrings on any given ring and compute the set of all hyperideals of related general hyperring. Moreover to...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2023, Vol.54 (1), p.120-132
Main Authors: Hamidi, Mohammad, Ameri, Reza, Mohammadi, Hoda
Format: Article
Language:English
Subjects:
Apexes
Applications of Mathematics
Graph theory
Graphs
Homomorphisms
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
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Summary:The purpose of this paper is to introduce the notion of intersection graphs based on non-trivial hyperideals in general hyperrings. In order to realise the article’s goals, we design general hyperrings on any given ring and compute the set of all hyperideals of related general hyperring. Moreover to establish of connection between of hyperideals as vertices of it’s associated graph, we introduce the concept of absorbing elements. The main method in this research is based on nonempty intersection of hyperideals, so we discuss on divisor of order of general hyperrings. As a result of the research, is constructing of some necessary and sufficient conditions in intersection graphs to be a connected( complete, Hamiltonian, or Eulerian) graph. Also, is presented notations of annihilator and kernel of homomorphisms via absorbing elements and fundamental relations. The paper includes implications for the development of intersection graph, for modelling the complex hypernetworks by absorbing elements, prime divisors and their relations in hyperideals. The new conception of intersection graphs based on hyperideals of general hyperrings was broached for the in this paper first time.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-022-00238-5