卡氏积图的Laplacian谱半径的上界
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摘要
对近年来图的Laplacian谱半径上界的研究成果进行了简单梳理.利用2个图的卡氏积图的特征值,讨论了2个循环图的卡氏积图的Laplacian谱半径的上界问题,得到了几个上界,推广了已有文献的结论.
We organize the results of the upper bounds of Laplacian spectral radius for some graphs in the last few years and explore the upper bounds of Laplacian spectral radius for the Cartesian product of circulant graphs based on the eigenvalues of the Cartesian product of two graphs.Our results generalize and improve the conclusion of the existing literatures.
We organize the results of the upper bounds of Laplacian spectral radius for some graphs in the last few years and explore the upper bounds of Laplacian spectral radius for the Cartesian product of circulant graphs based on the eigenvalues of the Cartesian product of two graphs.Our results generalize and improve the conclusion of the existing literatures.
引文
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[6]SHI L S.The spectral radius of irregular graphs[J].Linear Algebra and its Applications,2009,431:189-196.
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[10]GRONE R,MERRIS R,SUNDER V S.The Laplacian spectrum of a graph[J].SIAM Journal on Matrix Analysis and Applications,1990,11:218-238.
[11]LI J X,SHIU W C,CHAN W H.On the Laplacian spectral radii of bipartite graphs[J].Linear Algebra and its Applications,2011,435:2183-2192.
[12]PATRA K L,SAHOO B K,BHUBANESWAR.Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth[J].Czechoslovak Mathematical Journal,2013,63(138):909-922.
[13]周后卿.Cartesian积图的最大拉普拉斯特征值[J].邵阳学院学报,2011(1):5-7.ZHOU H Q.The largest eigenvalue of Laplacian matrix of cartesian product graph[J].Journal of Shaoyang University,2011(1):5-7.
[14]JIA H C,XUE J.On the Laplacian spectral radii of Halin graphs[J].Journal of Inequalities and Applications,2017:73.
[15]LIU M H,DAS K C,LAI H J.The(signless)Laplacian spectral radii of c-cyclic graphs with n vertices,girth gand k pendant vertices[J].Linear and Multilinear Algebra,2017,65(5):869-881.
[16]XING R D,ZHOU B.Laplacian and signless Laplacian spectral radii of graphs with fixed domination number[J].Mathematische Nachrichten,2015,288(4):476-480.
[17]CVETKOVIC D,DOOB M,SACHS H.Spectra of Graphs,Theory and Applications[M].Heidelberg:Johann Ambrosius Barth,1995.
[18]BELL F K,CVETKOVIC D,ROWLINSON P.Graphs for which the least eigenvalue is minimal[J].Linear Algebra and its Applications,2008,429:234-241.
[19]YU G D,FAN Y Z,WANG Y.The least eigenvalue of graphs[J].Journal of Mathematical Research with Applications,2012,32(6):659-665.
[2]ANDERSON W N,MORLEY T D.Eigenvalues of the Laplacian of a graph[J].Linear and Multilinear Algebra,1985,18:141-145.
[3]MERRIS R.A note on Laplacian graph eigenvalues[J].Linear Algebra and its Applications,1998,285:33-35.
[4]DAS K.An improved upper bound for Laplacian graph eigenvalues[J].Linear Algebra and its Applications.2003,368:269-278.
[5]LI J S,ZHANG X D.On the Laplacian eigenvalues of agraph[J].Linear Algebra and its Applications,1998,285:305-307.
[6]SHI L S.The spectral radius of irregular graphs[J].Linear Algebra and its Applications,2009,431:189-196.
[7]STEVANOVIC D.Bounding the largest eigenvalue of trees in terms of the largest vertex degree[J].Linear Algebra and its Applications,2003,360:35-42.
[8]GUO J M.On the Laplacian spectral radius of a tree[J].Linear Algebra and its Applications,2003,368:379-385
[9]FENG L H,YU G H,ILIC A.The Laplacian spectral radius for unicyclic graphs with given independence number[J].Linear Algebra and its Applications,2010,433:934-944.
[10]GRONE R,MERRIS R,SUNDER V S.The Laplacian spectrum of a graph[J].SIAM Journal on Matrix Analysis and Applications,1990,11:218-238.
[11]LI J X,SHIU W C,CHAN W H.On the Laplacian spectral radii of bipartite graphs[J].Linear Algebra and its Applications,2011,435:2183-2192.
[12]PATRA K L,SAHOO B K,BHUBANESWAR.Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth[J].Czechoslovak Mathematical Journal,2013,63(138):909-922.
[13]周后卿.Cartesian积图的最大拉普拉斯特征值[J].邵阳学院学报,2011(1):5-7.ZHOU H Q.The largest eigenvalue of Laplacian matrix of cartesian product graph[J].Journal of Shaoyang University,2011(1):5-7.
[14]JIA H C,XUE J.On the Laplacian spectral radii of Halin graphs[J].Journal of Inequalities and Applications,2017:73.
[15]LIU M H,DAS K C,LAI H J.The(signless)Laplacian spectral radii of c-cyclic graphs with n vertices,girth gand k pendant vertices[J].Linear and Multilinear Algebra,2017,65(5):869-881.
[16]XING R D,ZHOU B.Laplacian and signless Laplacian spectral radii of graphs with fixed domination number[J].Mathematische Nachrichten,2015,288(4):476-480.
[17]CVETKOVIC D,DOOB M,SACHS H.Spectra of Graphs,Theory and Applications[M].Heidelberg:Johann Ambrosius Barth,1995.
[18]BELL F K,CVETKOVIC D,ROWLINSON P.Graphs for which the least eigenvalue is minimal[J].Linear Algebra and its Applications,2008,429:234-241.
[19]YU G D,FAN Y Z,WANG Y.The least eigenvalue of graphs[J].Journal of Mathematical Research with Applications,2012,32(6):659-665.