Displaying similar documents to “On the signless Laplacian spectral characterization of the line graphs of T -shape trees”

Spectra of extended double cover graphs

Zhibo Chen (2004)

Czechoslovak Mathematical Journal

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The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph G with vertex set V = { v 1 , v 2 , ⋯ , v n } , the extended double cover of G , denoted G * , is the bipartite graph with bipartition ( X , Y ) where X = { x 1 , x 2 , ⋯ , x n } and Y = { y 1 , y 2 , ⋯ , y n } , in which x i and y j are adjacent iff i = j or v i and v j are adjacent in G . In this paper we obtain formulas for the characteristic polynomial and the spectrum of G * in terms of the corresponding information of G . Three formulas are derived for the number of spanning trees...

Some graphs determined by their (signless) Laplacian spectra

Muhuo Liu (2012)

Czechoslovak Mathematical Journal

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Let W n = K 1 ∨ C n - 1 be the wheel graph on n vertices, and let S ( n , c , k ) be the graph on n vertices obtained by attaching n - 2 c - 2 k - 1 pendant edges together with k hanging paths of length two at vertex v 0 , where v 0 is the unique common vertex of c triangles. In this paper we show that S ( n , c , k ) ( c ≥ 1 , k ≥ 1 ) and W n are determined by their signless Laplacian spectra, respectively. Moreover, we also prove that S ( n , c , k ) and its complement graph are determined by their Laplacian spectra, respectively, for c ≥ 0 and k ≥ 1 .

Rotation and jump distances between graphs

Gary Chartrand, Heather Gavlas, Héctor Hevia, Mark A. Johnson (1997)

Discussiones Mathematicae Graph Theory

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A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u,v, and w such that uv ∈ E(G), uw ∉ E(G), and H = G-uv+uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u,v,w, and x such that uv ∈ E(G), wx∉ E(G), and H = G-uv+wx. If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. It is shown that for every two graphs G and H of the same order (at least...

On graphs with the largest Laplacian index

Bo Lian Liu, Zhibo Chen, Muhuo Liu (2008)

Czechoslovak Mathematical Journal

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Let G be a connected simple graph on n vertices. The Laplacian index of G , namely, the greatest Laplacian eigenvalue of G , is well known to be bounded above by n . In this paper, we give structural characterizations for graphs G with the largest Laplacian index n . Regular graphs, Hamiltonian graphs and planar graphs with the largest Laplacian index are investigated. We present a necessary and sufficient condition on n and k for the existence of a k -regular graph G of order n with the...

On the Spectral Characterizations of Graphs

Jing Huang, Shuchao Li (2017)

Discussiones Mathematicae Graph Theory

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Several matrices can be associated to a graph, such as the adjacency matrix or the Laplacian matrix. The spectrum of these matrices gives some informations about the structure of the graph and the question “Which graphs are determined by their spectrum?” is still a difficult problem in spectral graph theory. Let [...] p2q 𝒰 p 2 q be the set of graphs obtained from Cp by attaching two pendant edges to each of q (q ⩽ p) vertices on Cp, whereas [...] p2q 𝒱 p 2 q the subset of [...] p2q 𝒰 p 2 q with odd p...