| 完全多部图的无符号Laplacian特征多项式(英文) |
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| 引用本文： | 卢世芳,赵海兴.完全多部图的无符号Laplacian特征多项式(英文)[J].数学季刊,2012(1):36-40. |
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| 作者姓名： | 卢世芳 赵海兴 |
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| 作者单位： | Department of Basic,Qinghai University;Department of Mathematics,Qinghai Normal University |
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| 基金项目： | Supported by the NSFC(60863006);Supported by the NCET(-06-0912);Supported by the Science-Technology Foundation for Middle-aged and Yong Scientist of Qinghai University(2011-QGY-8) |
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| 摘 要： | For a simple graph G,let matrix Q（G）=D（G） + A（G） be it’s signless Laplacian matrix and Q G （λ）=det（λI Q） it’s signless Laplacian characteristic polynomial,where D（G） denotes the diagonal matrix of vertex degrees of G,A（G） denotes its adjacency matrix of G.If all eigenvalues of Q G （λ） are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K（n1,n2,···,nt）.We prove that the complete t-partite graphs K（n,n,···,n）t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K（m,···,m）s（n,···,n）t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K（m,···,m,）s1（n,···,n,）s2（l,···,l）s3.
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| 关 键 词： | the signless Laplacian spectrum the complete multipartite graphs the Qintegral |
Signless Laplacian Characteristic Polynomials of Complete Multipartite Graphs |
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| LU Shi-fang,ZHAO Hai-xing.Signless Laplacian Characteristic Polynomials of Complete Multipartite Graphs[J].Chinese Quarterly Journal of Mathematics,2012(1):36-40. |
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| Authors: | LU Shi-fang ZHAO Hai-xing |
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| Institution: | 1.Department of Basic,Qinghai University,Xining 810016,China;2.Department of Mathematics,Qinghai Normal University,Xining 810008,China) |
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| Abstract: | For a simple graph G,let matrix Q（G）=D（G） + A（G） be it’s signless Laplacian matrix and Q G （λ）=det（λI Q） it’s signless Laplacian characteristic polynomial,where D（G） denotes the diagonal matrix of vertex degrees of G,A（G） denotes its adjacency matrix of G.If all eigenvalues of Q G （λ） are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K（n1,n2,···,nt）.We prove that the complete t-partite graphs K（n,n,···,n）t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K（m,···,m）s（n,···,n）t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K（m,···,m,）s1（n,···,n,）s2（l,···,l）s3. |
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| Keywords: | the signless Laplacian spectrum the complete multipartite graphs the Qintegral |
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