Permanental Bounds of the Laplacian Matrix of Trees with Given Domination Number

Geng, Xianya; Hu, Shuna; Li, Shuchao

doi:10.1007/s00373-014-1451-z

Cited by 10 publications

(3 citation statements)

References 25 publications

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“…The studies on Laplacian permanental polynomial mainly focus on two aspects, one is computing the coefficients of Laplacian permanental polynomial of a graph [1,4,7,8,10,17,13,15,20]. The other is distinguishing graphs by the Laplacian permanental polynomial.…”

Section: Introductionmentioning

confidence: 99%

The characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs

Wu¹,

Tian²

2022

Preprint

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Let G be a graph with n vertices, and let L(G) and Q(G) be the Laplacian matrix and signless Laplacian matrix of G, respectively. The polynomial π(L(G); x) = per(xI − L(G))) is called Laplacian permanental polynomial (resp. signless Laplacian permanental polynomial) of G. In this paper, we show that two classes of bicyclic graphs are determined by their (signless) Laplacian permanental polynomials.

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Section: Introductionmentioning

confidence: 99%

The characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs

Wu¹,

Tian²

2022

Preprint

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“…We call π(L(G), x) (resp, π(Q(G), x)) the Laplacian (resp, signless Laplacian) permanental polynomial of G. e Laplacian permanental polynomial of a graph was first considered by Merris et al [2], and the signless Laplacian permanental polynomial was first studied by Faria [3]. For more studies on (signless) Laplacian permanental polynomials, see [4][5][6][7][8][9][10][11][12][13][14], among others.…”

Section: Introductionmentioning

confidence: 99%

The Characterizing Properties of (Signless) Laplacian Permanental Polynomials of Almost Complete Graphs

Zhou

2021

Journal of Mathematics

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Let G be a graph with n vertices, and let L G and Q G denote the Laplacian matrix and signless Laplacian matrix, respectively. The Laplacian (respectively, signless Laplacian) permanental polynomial of G is defined as the permanent of the characteristic matrix of L G (respectively, Q G ). In this paper, we show that almost complete graphs are determined by their (signless) Laplacian permanental polynomials.

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“…Also he studied some special class of graphs with its dominating set [7]. In [8], Xianya Geng et al determined the first, second, third smallest Laplacian permanents of trees in the collection of all trees with n -vertices and with the domination number. Also they characterized the corresponding extremal graphs.…”

Section: Introductionmentioning

confidence: 99%

Matrix representation – Hajos stable graphs

Yamuna

Karthika

2017

IOP Conf. Ser.: Mater. Sci. Eng.

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Abstract. Binary operations are in general more difficult to implement when compared with unary operations. Normally any operation on a graph involves vertices or edges or both together. In general two graphs are involved in binary operation. Hajos construction is one such operation which involves vertices and edges with three operations. So two graphs with three operations on vertices and edges increases the difficulty in implanting it. Computation time increases when this operation is to be verified for all possible edge pairs between the two graphs. A matrix representation for this purpose would enable easy computation. In this paper we have provided a matrix method of verifying if two graphs are Hajos stable.

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Permanental Bounds of the Laplacian Matrix of Trees with Given Domination Number

Cited by 10 publications

References 25 publications

The characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs

The characterizing properties of (signless) Laplacian permanental polynomials of bicyclic graphs

The Characterizing Properties of (Signless) Laplacian Permanental Polynomials of Almost Complete Graphs

Matrix representation – Hajos stable graphs

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