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INTEGRAL LAPLACIAN GRAPHS WITH A UNIQUE REPEATED LAPLACIAN EIGENVALUE, II
INTEGRAL LAPLACIAN GRAPHS WITH A UNIQUE REPEATED LAPLACIAN EIGENVALUE, II
- 대한수학회
- Bulletin of the Korean Mathematical Society
- Vol.62No.2
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2025.01299 - 317 (19 pages)
- 0
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The multiset S<sub>{i,j}<sup>m</sup><sub>n</sub></sub> = {0, 1, 2, . . . , m - 1, m, m, m + 1, . . . , n - 1, n} \ {i, j}, 0 < i < j ⩽ n, is called Laplacian realizable if there exists a simple connected graph G whose Laplacian spectrum is S<sub>{i,j}<sup>m</sup><sub>n</sub></sub>. In this case, the graph G is said to realize S<sub>{i,j}<sup>m</sup><sub>n</sub></sub>. In this paper, we completely describe graphs realizing the multisets S<sub>{i,j}<sup>m</sup><sub>n</sub></sub> with m = 1, 2 and determine the structure of these graphs.
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