On Laplacian integrability of comaximal graphs of commutative rings
Publication details: New Delhi Springer 2024Edition: Vol.55(1), MarDescription: 310-324pSubject(s): Online resources: In: Indian journal of pure and applied mathematicsSummary: For a commutative ring R, the comaximal graph of R is a simple graph with vertex set R and two distinct vertices u and v of are adjacent if and only if . In this article, we find the Laplacian eigenvalues of and show that the algebraic connectivity of is always an even integer and equals , thereby giving a large family of graphs with integral algebraic connectivity. Further, we prove that the second largest Laplacian eigenvalue of is an integer if and only if and hence is Laplacian integral if and only if where p, q are primes and are non-negative integers. This answers a problem posed by [Banerjee, Laplacian spectra of comaximal graphs of the ring , Special Matrices, (2022)].| Item type | Current library | Status | Barcode | |
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School of Engineering & Technology Archieval Section | Not for loan | 2024-1567 |
For a commutative ring R, the comaximal graph of R is a simple graph with vertex set R and two distinct vertices u and v of are adjacent if and only if . In this article, we find the Laplacian eigenvalues of and show that the algebraic connectivity of is always an even integer and equals , thereby giving a large family of graphs with integral algebraic connectivity. Further, we prove that the second largest Laplacian eigenvalue of is an integer if and only if and hence is Laplacian integral if and only if where p, q are primes and are non-negative integers. This answers a problem posed by [Banerjee, Laplacian spectra of comaximal graphs of the ring , Special Matrices, (2022)].
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