On the construction of cospectral graphs for the adjacency and the normalized Laplacian matrices

Let G be a dihedral group and its conjugacy class graph. The Laplacian energy of the graph, is defined as the sum of the absolute values of the difference between the Laplacian eigenvalues and the ratio of twice the edges number divided by the vertices number. In this research, the Laplacian matrices of the conjugacy class graph of some dihedral groups, generalized quaternion groups, quasidihedral groups and their eigenvalues are first computed. Then, the Laplacian energy of the graphs are determined.

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Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Properties

SIAM Journal on Applied Mathematics ◽

10.1137/17m1124474 ◽

2018 ◽

Vol 78 (1) ◽

pp. 372-394 ◽

Cited By ~ 11

Author(s):

Camille Poignard ◽

Tiago Pereira ◽

Jan Philipp Pade

Keyword(s):

Weighted Graphs ◽

Laplacian Matrices

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The spectra of a new join of graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s179383091850074x ◽

2018 ◽

Vol 10 (06) ◽

pp. 1850074 ◽

Cited By ~ 2

Author(s):

Somnath Paul

Keyword(s):

Laplacian Spectrum ◽

Cospectral Graphs ◽

Signless Laplacian Spectrum ◽

Signless Laplacian ◽

Join Of Graphs ◽

Disjoint Sets

Let [Formula: see text] and [Formula: see text] be three graphs on disjoint sets of vertices and [Formula: see text] has [Formula: see text] edges. Let [Formula: see text] be the graph obtained from [Formula: see text] and [Formula: see text] in the following way: (1) Delete all the edges of [Formula: see text] and consider [Formula: see text] disjoint copies of [Formula: see text]. (2) Join each vertex of the [Formula: see text]th copy of [Formula: see text] to the end vertices of the [Formula: see text]th edge of [Formula: see text]. Let [Formula: see text] be the graph obtained from [Formula: see text] by joining each vertex of [Formula: see text] with each vertex of [Formula: see text] In this paper, we determine the adjacency (respectively, Laplacian, signless Laplacian) spectrum of [Formula: see text] in terms of those of [Formula: see text] and [Formula: see text] As an application, we construct infinite pairs of cospectral graphs.

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