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Keywords = anti-reciprocal eigenvalue property

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18 pages, 1914 KB  
Article
Spectral Characterization of Graphs with Respect to the Anti-Reciprocal Eigenvalue Property
by Hao Guan, Aysha Khan, Sadia Akhter and Saira Hameed
Symmetry 2023, 15(6), 1240; https://doi.org/10.3390/sym15061240 - 10 Jun 2023
Cited by 3 | Viewed by 2237
Abstract
Let G=(V,E) be a simple connected graph with vertex set V and edge set E, respectively. The term “anti-reciprocal eigenvalue property“ refers to a non-singular graph G for which, [...] Read more.
Let G=(V,E) be a simple connected graph with vertex set V and edge set E, respectively. The term “anti-reciprocal eigenvalue property“ refers to a non-singular graph G for which, 1λσ(G), whenever λσ(G), λσ(G). Here, σ(G) is the multiset of all eigenvalues of A(G). Moreover, if multiplicities of eigenvalues and their negative reciprocals are equal, then that graph is said to have strong anti-reciprocal eigenvalue properties, and the graph is referred to as a strong anti-reciprocal graph (or (SR) graph). In this article, a new family of graphs Fn(k,j) is introduced and the energy of F5(k,k2)k2 is calculated. Furthermore, with the help of F5(k,k2), some families of (SR) graphs are constructed. Full article
(This article belongs to the Special Issue Symmetric Matrices of Graphs: Topics and Advances)
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