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Spectral analysis of a graph on the special set 풮.
- Source :
-
Discrete Mathematics, Algorithms & Applications . Feb2024, p1. 22p. - Publication Year :
- 2024
-
Abstract
- Let ℤn be the ring of integer modulo n with two binary operators, addition (+) and multiplication (.), where n is a positive integer. The special set 풮 is defined as 풮 = {a ∈ ℤn : (∃b ∈ ℤn) ba ≡ a, b≢a, b≢1}. Our purpose in the present paper is to propose a new family of interconnection networks that are Cayley graphs on this special set 풮 and denote it by Ω−(Z n). In this paper, we define a relationship between G and Ge∗, Ge∗ is a derived graph from G by removing r edges, where r is a known fixed value. We also give the spectrum of absorption Cayley graph, unitary addition Cayley graph, and Ω−(Z n). We also provide values of n for which the graph Ω−(ℤ n) is hyperenergetic and discuss the structural properties of this graph, such as planarity and connectedness. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17938309
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics, Algorithms & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 175397319
- Full Text :
- https://doi.org/10.1142/s1793830924500071