循环图的无符号Laplacian能量的上界
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摘要
给出一个图G,称矩阵Q=D+A为无符号Laplacian矩阵,其中A表示G的邻接矩阵,D表示G的顶点度的对角矩阵.定义无符号Laplacian能量为矩阵Q的特征值与图的顶点度的算术平均值的差的绝对值之和.研究了循环图的无符号Laplacian能量的上界,得到了几个有意义的结果.
Given a graph G,the matrix Q=D+A is called the signless Laplacian matrix,where A is the adjacency matrix and D is the diagonal matrix of vertex degrees.The signless Laplacian energy is the sum of the absolute values of the differences between the eigenvalues of matrix Q and the arithmetic mean of the vertex degrees of the graph.We discuss the upper bounds of signless Laplacians energy for circulant graphs,and get some significant results.
Given a graph G,the matrix Q=D+A is called the signless Laplacian matrix,where A is the adjacency matrix and D is the diagonal matrix of vertex degrees.The signless Laplacian energy is the sum of the absolute values of the differences between the eigenvalues of matrix Q and the arithmetic mean of the vertex degrees of the graph.We discuss the upper bounds of signless Laplacians energy for circulant graphs,and get some significant results.
引文
[1]CVETKOVI C′DRAGOS,ROWLINSON PETER,SIMI C′SLOBODAN K.Signless Laplacians of Finite Graphs[J].Linear Algebra and Its Applications,2007,423(1):155-171.
[2]CVETKOVI C′DRAGOS,SIMI C′SLOBODAN K.Towards a Spectral Theory of Graphs Based on the Signless Laplacian,I[J].Publications de l’Institut Mathematique,2009,85(99):19-33.
[3]CVETKOVI C′DRAGOS,SIMI C′SLOBODAN K.Towards a Spectral Theory of Graphs Based on the Signless Laplacian,II[J].Linear Algebra and Its Applications,2010,432(9):2 257-2 272.
[4]CVETKOVI C′DRAGOS,SIMI C′SLOBODAN K.Towards a Spectral Theory of Graphs Based on the Signless Laplacian,III[J].Applicable Analysis and Discrete Mathematics,2010,4(1):156-166.
[5]ZHANG Xiaodong.The Signless Laplacian Spectral Radius of Graphs with Given Degree Sequence[J].Discrete Applied Mathematics,2009,157(13):2 928-2 937.
[6]LIU Muhuo,TAN Xuezhong,LIU Bolian.The(Signless)Laplacian Spectral Radius of Unicyclic and Bicyclic Graphs with n Vertices and k Pendant Vertices[J].Czechoslovak Mathematical Journal,2010,60(3):849-867.
[7]MIRZAKHAH MARYAM,KIANI DARIUSH.Some Results on Signless Laplacian Coefficients of Graphs[J].Linear Algebra and Its Applications,2012,437(9):2 243-2 251.
[8]PINHEIRO LUCELIA KOWALSKI,TREVISAN VILMAR.Maximality of the Signless Laplacian Energy[J].Discrete Mathematics,2018,341(1):33-41.
[9]DAS KINKAR CH,MOJALLAL SEYED AHMAD.Relation Between Signless Laplacian Energy,Energy of Graph and Its Line Graph[J].Linear Algebra and Its Applications,2016,493:91-107.
[10]BINTHIYA R,SARASIJA P B.On the Signless Laplacian Energy and Signless Laplacian Estrada Index of Extremal Graphs[J].Applied Mathematical Sciences,2014,8:193-198.
[11]ABREU NAIR,CARDOSO DOMINGOS M,GUTMAN IVAN,et al.Bounds for the Signless Laplacian Energy[J].Linear Algebra and Its Applications,2011,435(10):2 365-2 374.
[12]DAS K C,MOJALLAL S AHMAD.Relation Between Energy and(Signless)Laplacian Energy of Graphs[J].MATCH Communications in Mathematical and in Computer Chemistry,2015,74:359-366.
[13]周后卿,周琪.循环图能量的一个上界[J].应用数学,2013,26(2):451-457.
[14]LI Rao.New Upper Bounds for the Energy and Signless Laplacian Energy of Agraph[J].International Journal of Advances in Applied Mathematics and Mechanics,2015,3(1):24-27.
[2]CVETKOVI C′DRAGOS,SIMI C′SLOBODAN K.Towards a Spectral Theory of Graphs Based on the Signless Laplacian,I[J].Publications de l’Institut Mathematique,2009,85(99):19-33.
[3]CVETKOVI C′DRAGOS,SIMI C′SLOBODAN K.Towards a Spectral Theory of Graphs Based on the Signless Laplacian,II[J].Linear Algebra and Its Applications,2010,432(9):2 257-2 272.
[4]CVETKOVI C′DRAGOS,SIMI C′SLOBODAN K.Towards a Spectral Theory of Graphs Based on the Signless Laplacian,III[J].Applicable Analysis and Discrete Mathematics,2010,4(1):156-166.
[5]ZHANG Xiaodong.The Signless Laplacian Spectral Radius of Graphs with Given Degree Sequence[J].Discrete Applied Mathematics,2009,157(13):2 928-2 937.
[6]LIU Muhuo,TAN Xuezhong,LIU Bolian.The(Signless)Laplacian Spectral Radius of Unicyclic and Bicyclic Graphs with n Vertices and k Pendant Vertices[J].Czechoslovak Mathematical Journal,2010,60(3):849-867.
[7]MIRZAKHAH MARYAM,KIANI DARIUSH.Some Results on Signless Laplacian Coefficients of Graphs[J].Linear Algebra and Its Applications,2012,437(9):2 243-2 251.
[8]PINHEIRO LUCELIA KOWALSKI,TREVISAN VILMAR.Maximality of the Signless Laplacian Energy[J].Discrete Mathematics,2018,341(1):33-41.
[9]DAS KINKAR CH,MOJALLAL SEYED AHMAD.Relation Between Signless Laplacian Energy,Energy of Graph and Its Line Graph[J].Linear Algebra and Its Applications,2016,493:91-107.
[10]BINTHIYA R,SARASIJA P B.On the Signless Laplacian Energy and Signless Laplacian Estrada Index of Extremal Graphs[J].Applied Mathematical Sciences,2014,8:193-198.
[11]ABREU NAIR,CARDOSO DOMINGOS M,GUTMAN IVAN,et al.Bounds for the Signless Laplacian Energy[J].Linear Algebra and Its Applications,2011,435(10):2 365-2 374.
[12]DAS K C,MOJALLAL S AHMAD.Relation Between Energy and(Signless)Laplacian Energy of Graphs[J].MATCH Communications in Mathematical and in Computer Chemistry,2015,74:359-366.
[13]周后卿,周琪.循环图能量的一个上界[J].应用数学,2013,26(2):451-457.
[14]LI Rao.New Upper Bounds for the Energy and Signless Laplacian Energy of Agraph[J].International Journal of Advances in Applied Mathematics and Mechanics,2015,3(1):24-27.