Laplacian integral graphs with a given degree sequence constraint
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Let G be a graph on n vertices. The Laplacian matrix of G, denoted by L(G), is defined as L(G) = D(G) −A(G), where A(G) is the adjacency matrix of G and D(G) is the diagonal matrix of the vertex degrees of G. A graph G is said to be L-integral if all eigenvalues of the matrix L(G) are integers. In this paper, we characterize all Lintegral non-bipartite graphs among all connected graphs with at most two vertices of degree larger than or equal to three.
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2017 ◽
Vol 32
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pp. 217-231
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2019 ◽
Vol 11
(01)
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pp. 1950001
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