Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897934 | Linear Algebra and its Applications | 2018 | 14 Pages |
Abstract
The complementary prism GGâ¾ of a graph G is obtained from the disjoint union of G and its complement Gâ¾ by adding an edge for each pair of vertices (v,vâ²), where v is in G and its copy vâ² is in Gâ¾. The Petersen graph C5C5â¾ and, for nâ¥2, the corona product of Kn and K1 which is KnKnâ¾ are examples of complementary prisms. This paper is devoted to the computation of eigenpairs of the adjacency, signless Laplacian and Laplacian matrices of a complementary prism GGâ¾ in terms of the eigenpairs of the corresponding matrices of G. Particular attention is given to the complementary prisms of regular graphs. Furthermore, Petersen graph is shown to be the unique complementary prism which is a strongly regular graph.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Domingos M. Cardoso, Paula Carvalho, Maria Aguieiras A. de Freitas, Cybele T.M. Vinagre,