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An inequality using perfect matchings and laplacian spread of a graph
, Article Linear and Multilinear Algebra ; Volume 67, Issue 3 , 2019 , Pages 442-447 ; 03081087 (ISSN) ; Fath-Tabar, G. H ; Ghasemian, E ; Sharif University of Technology
Taylor and Francis Ltd
2019
Abstract
Let G be a simple connected graph of order n. Let (Formula presented.) be the Laplacian eigenvalues of G. In this paper, we show that if X and Y are two subsets of vertices of G such that (Formula presented.) and the set of all edges between X and Y decomposed into r disjoint perfect matchings, then, (Formula presented.) where (Formula presented.). Also, we determine a relation between the Laplacian eigenvalues and matchings in a bipartite graph by showing that if (Formula presented.) is a bipartite graph, (Formula presented.) and (Formula presented.), then G has a matching that saturates U. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; 2019 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2019
Abstract
For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; 2019 ; 03081087 (ISSN) ; Akbari, S
Taylor and Francis Ltd
2019
Abstract
For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; Volume 69, Issue 7 , 2021 , Pages 1248-1254 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2021
Abstract
For a graph G, let (Formula presented.) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019 Informa UK Limited, trading as Taylor & Francis Group
A note on the algebraic connectivity of a graph and its complement
, Article Linear and Multilinear Algebra ; Volume 69, Issue 7 , 2021 , Pages 1248-1254 ; 03081087 (ISSN) ; Akbari, S ; Sharif University of Technology
Taylor and Francis Ltd
2021
Abstract
For a graph G, let (Formula presented.) denote its second smallest Laplacian eigenvalue. It was conjectured that (Formula presented.), where (Formula presented.) is the complement of G. In this paper, it is shown that (Formula presented.). © 2019 Informa UK Limited, trading as Taylor & Francis Group