Laplacian energy of generalized complements of a graph

H. J. Gowtham, Sabitha D'Souza, Pradeep G. Bhat

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let P = [V1, V2, V3, . . ., Vk] be a partition of vertex set V (G) of order k ≥ 2. For all Vi and Vj in P, i ≠ j, remove the edges between Vi and Vj in graph G and add the edges between Vi and Vj which are not in G. The graph Gk P thus obtained is called the k-complement of graph G with respect to a partition P. For each set Vr in P, remove the edges of graph G inside Vr and add the edges of G (the complement of G) joining the vertices of Vr. The graph Gk(i) P thus obtained is called the k(i)-complement of graph G with respect to a partition P. In this paper, we study Laplacian energy of generalized complements of some families of graph. An effort is made to throw some light on showing variation in Laplacian energy due to changes in a partition of the graph.

Original languageEnglish
Pages (from-to)299-315
Number of pages17
JournalKragujevac Journal of Mathematics
Volume42
Issue number2
Publication statusPublished - 01-01-2018

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Complement
Graph in graph theory
Energy
Partition
Joining
Vertex of a graph

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Gowtham, H. J. ; D'Souza, Sabitha ; Bhat, Pradeep G. / Laplacian energy of generalized complements of a graph. In: Kragujevac Journal of Mathematics. 2018 ; Vol. 42, No. 2. pp. 299-315.
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Laplacian energy of generalized complements of a graph. / Gowtham, H. J.; D'Souza, Sabitha; Bhat, Pradeep G.

In: Kragujevac Journal of Mathematics, Vol. 42, No. 2, 01.01.2018, p. 299-315.

Research output: Contribution to journalArticle

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