Laplacian integral graphs with a given degreee sequence constraint

• Novanta, Anderson Fernandes ^[2] ; Oliveira, Carla Silva ^[3] ; de Lima, Leonardo Silva ^[1]
  1. [1] Universidade Federal do Paraná

     Universidade Federal do Paraná

     Brasil

     
  2. [2] Centro Federal de Educação Tecnológica Celso Suckow da Fonseca.
  3. [3] Escola Nacional de Ciências Estatísticas.

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 6, 2021, págs. 1431-1448
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4735
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• Resumen

  • 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 is all eigenvalues of the matrix L(G) are integers. In this paper, we characterize all L-integral non-bipartite graphs among all connected graphs with at most two vertices of degree larger than or equal to three.

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