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New families of Laplacian borderenergetic graphs

Dede, Cahit

Acta informatica, 2024-06, Vol.61 (2), p.115-129 [Periódico revisado por pares]

Berlin/Heidelberg: Springer Berlin Heidelberg

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  • Título:
    New families of Laplacian borderenergetic graphs
  • Autor: Dede, Cahit
  • Assuntos: Computer Science ; Computer Systems Organization and Communication Networks ; Data Structures and Information Theory ; Eigenvalues ; Energy ; Graphs ; Information Systems and Communication Service ; Laplace transforms ; Logics and Meanings of Programs ; Original Article ; Software Engineering/Programming and Operating Systems ; Theory of Computation
  • É parte de: Acta informatica, 2024-06, Vol.61 (2), p.115-129
  • Descrição: Laplacian matrix and its spectrum are commonly used for giving a measure in networks in order to analyse its topological properties. In this paper, Laplacian matrix of graphs and their spectrum are studied. Laplacian energy of a graph G of order n is defined as LE ( G ) = ∑ i = 1 n | λ i ( L ) - d ¯ | , where λ i ( L ) is the i -th eigenvalue of Laplacian matrix of G , and d ¯ is their average. If LE ( G ) = LE ( K n ) for the complete graph K n of order n , then G is known as L -borderenergetic graph. In the first part of this paper, we construct three infinite families of non-complete disconnected L -borderenergetic graphs: Λ 1 = { G b , j , k = [ ( ( ( j - 2 ) k - 2 j + 2 ) b + 1 ) K ( j - 1 ) k - ( j - 2 ) ] ∪ b ( K j × K k ) | b , j , k ∈ Z + } , Λ 2 = { G 2 , b = [ K 6 ∇ b ( K 2 × K 3 ) ] ∪ ( 4 b - 2 ) K 9 | b ∈ Z + } , Λ 3 = { G 3 , b = [ b K 8 ∇ b ( K 2 × K 4 ) ] ∪ ( 14 b - 4 ) K 8 b + 6 | b ∈ Z + } , where ∇ is join operator and × is direct product operator on graphs. Then, in the second part of this work, we construct new infinite families of non-complete connected L -borderenergetic graphs Ω 1 = { K 2 ∇ a K 2 r ¯ | a ∈ Z + } , Ω 2 = { a K 3 ∪ 2 ( K 2 × K 3 ) ¯ | a ∈ Z + } and Ω 3 = { a K 5 ∪ ( K 3 × K 3 ) ¯ | a ∈ Z + } , where G ¯ is the complement operator on G .
  • Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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